This site is supported by donations to The OEIS Foundation.

CiteR

From OeisWiki
Jump to: navigation, search


"We must mention that an invaluable resource while dealing with integer sequences is the Online Encyclopedia of Integer Sequences." [Anandaroop Ray et al., 2018]

"We are grateful to the OEIS Foundation Inc. for maintaining an extremely useful online encyclopedia of integer sequences" [Sten A. Reijers, 2019]

"The On-Line Encyclopedia of Integer Sequences OEIS is an incredibly valuable tool in mathematical research. As a ‘fingerprint database for theorems’ it allows to identify interconnections and relations between theorems throughout mathematics. In this spirit, FindStat is a collaborative online database of combinatorial statistics on combinatorial collections and of combinatorial maps between such collections." [Martin Rubey and Christian Stump, 2019]

About this page

  • This is part of the series of OEIS Wiki pages that list works citing the OEIS.
  • Additions to these pages are welcomed.
  • But if you add anything to these pages, please be very careful — remember that this is a scientific database. Spell authors' names, titles of papers, journal names, volume and page numbers, etc., carefully, and preserve the alphabetical ordering.
  • If you are unclear about what to do, contact one of the Editors-in-Chief before proceeding.
  • Works are arranged in alphabetical order by author's last name.
  • Works with the same set of authors are arranged by date, starting with the oldest.
  • This section lists works in which the first author's name begins with R.
  • The full list of sections is: A Ba Bi Ca Ci D E F G H I J K L M N O P Q R Sa Sl T U V W X Y Z.
  • For further information, see the main page for Works Citing OEIS.

References

  1. Sunil Kumar R and K Balakrishnan, Betweenness Centrality of Cartesian Product of Graphs, arXiv preprint arXiv:1603.04258, 2016.
  2. Martin Raab, Large gaps between primes in arithmetic progressions — an empirical approach, arXiv:2203.02276 [math.NT], 2022.
  3. Julius F. T. Rabago, On the Closed-Form Solution of a Nonlinear Difference Equation and Another Proof to Sroysang's Conjecturem arXiv preprint arXiv:1604.06659, 2016.
  4. Heinz-Joachim Rack and Robert Vajda, Explicit algebraic solution of Zolotarev's First Problem for low-degree polynomials, Part II, Dolomites Res. Notes Approxim., Func. Anal., Approxim. Theor. Num. Anal., (FAATNA20>22, 2023) Vol. 16, 75-103. PDF (A000010)
  5. D. G. Radcliffe, The growth of digital sums of powers of two, https://radcliffe.github.io/digitsumpower2.pdf, Preprint 2015. Also arXiv preprint arXiv:1605.02839, 2016.
  6. Jamie Radcliffe and Adam Volk, Generalized saturation problems for cliques, paths, and stars, arXiv:2101.04213 [math.CO], 2021. (A001571)
  7. Adityanarayanan Radhakrishnan, Liam Solus, Caroline Uhler, Counting Markov Equivalence Classes by Number of Immoralities, arXiv preprint arXiv:1611.07493v2, 2016. Official publication: http://auai.org/uai2017/proceedings/papers/97.pdf
  8. Yan Alves Radtke, Stefan Felsner, Johannes Obenaus, Sandro Roch, Manfred Scheucher, and Birgit Vogtenhuber, Flip Graph Connectivity for Arrangements of Pseudolines and Pseudocircles, arXiv:2310.19711 [math.CO], 2023. (A006245, A296406)
  9. Y. Raekow, A taxonomy of non-cooperatively computable functions, Presented at WEWoRC 2011.
  10. Paul Raff, arXiv:0809.2551 Spanning Trees in Grid Graphs
  11. Kari Ragnarsson and Bridget Eileen Tenner, Obtainable Sizes of Topologies on Finite Sets (2008); arXiv:0802.2550; Journal of Combinatorial Theory, Series A 117 (2010) 138-151 doi:10.1016/j.jcta.2009.05.002
  12. Kari Ragnarsson and Bridget Eileen Tenner, Homotopy Type of the Boolean Complex of a Coxeter System (2008); arXiv:0806.0906; Advances in Mathematics 222 (2009) 409-430 doi:10.1016/j.aim.2009.05.007
  13. Ragnarsson, Kári; Tenner, Bridget Eileen, Homology of the Boolean complex. J. Algebraic Combin. 34 (2011), no. 4, 617-639.
  14. Marco Ragni and Andreas Klein, Predicting Numbers: An AI Approach to Solving Number Series, Lecture Notes in Computer Science, 2011, Volume 7006, Advances in Artificial Intelligence, Pages 255-259; doi:10.1007/978-3-642-24455-1_24.
  15. M. Ragni, G. Strube, Cognitive Complexity and Analogies in Transfer Learning, KI-Künstliche Intelligenz, 2013; doi:10.1007/s13218-013-0288-6
  16. M. Rahmani, The Akiyama-Tanigawa matrix and related combinatorial identities, Linear Algebra and its Applications 438 (2013) 219-230.
  17. Alexander Rahn, Max Henkel, Sourangshu Ghosh, Eldar Sultanow, and Idriss Aberkane, An algorithm for linearizing Collatz convergence, hal-03286608 [math.DS], 2021. Abstract (A005184, A006370)
  18. Jay Rahn, The Hurrian Pieces, ca. 1350 BCE: Part Two, From Numbered Strings to Tuned Strings; http://aawmjournal.com/articles/2011b/Rahn_AAWM_Vol_1_2.pdf
  19. Jay Rahn, Coordinating Analyses of Tunings with Analyses of Pieces, Fourth International Conference on Analytical Approaches to World Music (2016)
  20. E. M. Rains and N. J. A. Sloane, "On Cayley's Enumeration of Alkanes (or 4-Valent Trees)", J. Integer Sequences, Volume 2, 1999, Article 99.1.1.
  21. E. M. Rains, N. J. A. Sloane and J. Stufken, The Lattice of N-Run Orthogonal Arrays, J. Statist. Planning Inference, 102 (2002), 477-500, doi:10.1016/S0378-3758(01)00119-7
  22. C. Raissi and J. Pei, Towards Bounding Sequential Patterns, http://www.cs.sfu.ca/~jpei/publications/SeqPatternBound-KDD11.pdf.
  23. A. Rajan, A. Rao, R. V. Rao, H. S. Jamadagni, Gaussian Approximation Using Integer Sequences, Advances in Signal Processing and Intelligent Recognition Systems, Advances in Intelligent Systems and Computing, Volume 264, 2014, pp. 213-224.
  24. Arulalan Rajan, R. Vittal Rao, Ashok Rao and H. S. Jamadagni, Fibonacci Sequence, Recurrence Relations, Discrete Probability Distributions and Linear Convolution, Arxiv preprint arXiv:1205.5398, 2012.
  25. Samyak Rajanala and Julia A. Palacios, Statistical summaries of unlabelled evolutionary trees and ranked hierarchical clustering trees, arXiv:2106.02724 [stat.ME], 2021. (A000111)
  26. Aayush Rajasekaran, Using Automata Theory to Solve Problems in Additive Number Theory, MS thesis, University of Waterloo, 2018. PDF (A000045, A003662, A003849, A006995, A020330, A175468)
  27. Aayush Rajasekaran, Narad Rampersad, Jeffrey Shallit, Overpals, Underlaps, and Underpals, In: Brlek S., Dolce F., Reutenauer C., Vandomme É. (eds) Combinatorics on Words, WORDS 2017, Lecture Notes in Computer Science, vol 10432. doi:10.1007/978-3-319-66396-8_3
  28. Aayush Rajasekaran, Jeffrey Shallit, and Tim Smith, Sums of Palindromes: an Approach via Automata, arXiv:1706.10206 [cs.FL], 2017.
  29. Aayush Rajasekaran, Jeffrey Shallit, Tim Smith, Additive Number Theory via Automata Theory, Theory of Computing Systems (2019) 1–26. doi:10.1007/s00224-019-09929-9 (A000069, A006995)
  30. Rakshith Rajashekar, Marco Di Renzo, K.V.S. Hari, L. Hanzo, A generalised transmit and receive diversity condition for feedback assisted MIMO systems: theory & applications in full-duplex spatial modulation</a>, 2017. PDF (A013595)
  31. Rajkovic, Predrag M.; Petkovic, Marko D.; Barry, Paul, The Hankel transform of the sum of consecutive generalized Catalan numbers. Integral Transforms Spec. Funct. 18 (2007), no. 3-4, 285-296.
  32. Chetansing Rajput, Metallic Ratios: Beyond the Golden Ratio, The Mathematical Relationships between different Metallic Means, J. of Advances in Math. (2021) Vol 20, 158-166. doi:10.24297/jam.v20i.9023 (A000045, A000129, A000204, A002203)
  33. Paul M. Rakotomamonjy, Sandrataniaina R. Andriantsoa, Arthur Randrianarivony, Crossings over permutations avoiding some pairs of three length-patterns, arXiv:1910.13809 [math.CO], 2019. (A076791, A299927)
  34. Paul M. Rakotomamonjy, Sandrataniaina R. Andriantsoa, Arthur Randrianarivony, Crossings over Permutations Avoiding Some Pairs of Patterns of Length Three, J. Int. Seq., Vol. 23 (2020), Article 20.6.3. HTML (A007318, A076791, A299927)
  35. Dimbinaina Ralaivaosaona, Jean Bernoulli Ravelomanana, Stephan Wagner, Counting Planar Tanglegrams, LIPIcs Proceedings of Analysis of Algorithms 2018, Vol. 110. Schloss Dagstuhl-Leibniz-Zentrum fuer Informatik, 2018. doi:10.4230/LIPIcs.AofA.2018.32 (A257887, A258620)
  36. Franck Ramaharo, Enumerating the states of the twist knot, arXiv:1712.06543 [math.CO], 2017. (A000124, A001477, A005408, A014206, A064999)
  37. Franck Ramaharo, An approximate Jerusalem square whose side equals a Pell number, arXiv:1801.00466v1 [math.CO], 1 Jan 2018
  38. Franck Ramaharo, Statistics on some classes of knot shadows, arXiv:1802.07701 [math.CO], 2018. (A000012, A000244, A001477, A001787, A002696, A004310, A004311, A004319, A005408, A005843, A006566, A007318, A008585, A008586, A014206, A027471, A028326, A034870, A036289, A038208, A054556, A062741, A064999, A069835, A080855, A120908, A130883, A139272, A139548, A140066, A143689, A152947, A167667, A212697, A258935, A295077)
  39. Franck Ramaharo, A generating polynomial for the pretzel knot. arXiv:1805.10680 [math.CO], 2018. (A000290, A000312, A000984, A006566, A007318, A010054, A023531, A038208, A062741, A073424, A083374, A097805, A104002, A130883, A152947, A154272, A178208, A295077, A299989, A300184, A300451)
  40. Franck Ramaharo, A one-variable bracket polynomial for some Turk's head knots, arXiv:1807.05256 [math.CO], 2018. (A004146, A060867, A099920, A122076, A300184, A300192, A300454)
  41. Franck Ramaharo, A generating polynomial for the two-bridge knot with Conway's notation C(n,r), arXiv:1902.08989 [math.CO], 2019. (A000124, A007318, A014206, A077028, A233583, A294619, A300401, A300453, A300454, A321125, A321126, A321127)
  42. Franck Ramaharo, Fanja Rakotondrajao, A state enumeration of the foil knot, arXiv:1712.04026 [math.CO], 2017. (A000004, A000012, A000124, A001477)
  43. Franck Ramaharo, Note on sequences A123192, A137396 and A300453, arXiv:1911.04528 [math.CO], 2019. (A123192, A137396, A300453)
  44. Franck Ramaharo, A bracket polynomial for 2-tangle shadows, arXiv:2002.06672 [math.CO], 2020. (A007318, A034870, A038208, A129185, A139548, A299989, A300184, A300192, A300453)
  45. Silvana Ramaj, New Results on Cyclic Compositions and Multicompositions, Master's Thesis, Georgia Southern Univ., 2021. PDF (A000079, A000358, A001792, A008965, A032189, A034738, A049610, A059570, A081038, A081039, A081040, A081041, A081042, A093305, A105476, A159612, A162770, A189732, A280218, A306897) The On-Line Encyclopedia of Integer Sequences (OEIS) [16] has been an important reference in what is known about particular sequences generated in this paper.
  46. Vignesh Raman, The Generalized Superfactorial, Hyperfactorial and Primorial functions, arXiv:2012.00882 [math.NT], 2020. (A000178, A002109)
  47. Olivier Ramaré, An “Algebraical” Multiplicative Function, Excursions in Multiplicative Number Theory, Birkhäuser Advanced Texts, Basler Lehrbücher, Birkhäuser, Cham (2022), 55. doi:10.1007/978-3-030-73169-4_5
  48. Olivier Ramaré, Primes in Arithmetical Progressions, Excursions in Multiplicative Number Theory, Birkhäuser Advanced Texts, Basler Lehrbücher, Birkhäuser, Cham (2022), 162. doi:10.1007/978-3-030-73169-4_15
  49. Olivier Ramaré, Computing a Famous Constant, Excursions in Multiplicative Number Theory, Birkhäuser Advanced Texts, Basler Lehrbücher, Birkhäuser, Cham (2022), 169–171. doi:10.1007/978-3-030-73169-4_16
  50. Olivier Ramaré, S. Ettahri, and L. Surel, Fast multi-precision computation of some Euler products, Mathematics of Computation (2021) hal-03381427. Abstract (A003136, A301429, A301430)
  51. Sanjay Ramassamy, Extensions of partial cyclic orders, Euler numbers and multidimensional boustrophedons, arXiv:1706.03386 [math.CO], 2017.
  52. Sanjay Ramassamy, Modular periodicity of the Euler numbers and a sequence by Arnold, arXiv:1712.08666 [math.CO], 2017. (A108039)
  53. Naren Ramesh, Generalising the configurations of an N × N × N Rubik's Cube, Parabola (2023) Vol. 59, Issue 3. See p. 22. Abstract (A075152)
  54. V. Arvind Rameshwar, Shreyas Jain, and Navin Kashyap, Sampling-Based Estimates of the Sizes of Constrained Subcodes of Reed-Muller Codes, arXiv:2309.08907 [cs.IT], 2023. (A048651)
  55. V. Arvind Rameshwar and Navin Kashyap, Estimating the Sizes of Binary Error-Correcting Constrained Codes, arXiv:2301.05098 [cs.IT], 2023. (A000031)
  56. Sanjaye Ramgoolam, Permutation Invariant Gaussian Matrix Models, arXiv:1809.07559 [hep-th], 2018. (A052171)
  57. José L. Ramírez, Some Combinatorial Properties of the k-Fibonacci and the k-Lucas Quaternions, An. Şt. Univ. Ovidius Constanţa, vol. 23 (2), 2015, 201-212. (A000045, A000032)
  58. José L. Ramírez, The Pascal Rhombus and the Generalized Grand Motzkin Paths, arXiv:1511.04577 [math.CO], 2015.
  59. J. L. Ramírez, G. N. Rubiano, Properties and Generalizations of the Fibonacci Word Fractal, The Mathematica J., Vol. 16 (2014).
  60. J. L. Ramirez, G. N. Rubiano and R. de Castro, A Generalization of the Fibonacci Word Fractal and the Fibonacci Snowflake, arXiv preprint arXiv:1212.1368, 2012.
  61. Jose L. Ramirez, M Shattuck, A (p, q)-Analogue of the r-Whitney-Lah Numbers, Journal of Integer Sequences, 19, 2016, #16.5.6.
  62. José L. Ramirez, Mark Shattuck, Generalized Jacobsthal numbers and restricted k-ary words, Pure Mathematics and Applications (2019) Vol. 28, Issue 1, 91-108. doi:10.1515/puma-2015-0034 (A000045)
  63. J. L. Ramirez and V. F. Sirvent, Incomplete Tribonacci Numbers and Polynomials, Journal of Integer Sequences, Vol. 17, 2014, #14.4.2.
  64. J. L. Ramírez, V. F. Sirvent, A Generalization of the k-Bonacci Sequence from Riordan Arrays, The Electronic Journal of Combinatorics, 22(1) (2015), #P1.38
  65. Philippe Ramirez, Stéphane Legendre, Revisiting asymmetric marriage rules, in Soc. Netw. 52 (2017), pp. 261-269. doi:10.1016/j.socnet.2017.09.004
  66. Jan-Paul V. Ramos, Pythagorean Triples in the Pascal Triangle: A computational and algebraic approach, University Gardens High School, San Juan, Puerto Rico, 2021. PDF (A000217)
  67. Narad Rampersad, Manon Stipulanti, The Formal Inverse of the Period-Doubling Sequence, arXiv:1807.11899 [math.CO], 2018. (A079523, A096268, A121539, A317542, A317543, A317544)
  68. Narad Rampersad and Elise Vaslet, "On Highly Repetitive and Power Free Words", Journal of Integer Sequences, Vol. 16 (2013), #13.2.7.
  69. Narad Rampersad and Max Wiebe, Sums of products of binomial coefficients mod 2 and 2-regular sequences, arXiv:2309.04012 [math.NT], 2023. (A000027, A000045, A000079, A000930, A008619, A040000, A086747, A329723)
  70. J. Ramsden and H. Sharipov, Inverse problems associated with perfect cuboids, Arxiv preprint arXiv:1207.6764, 2012
  71. J. Ramsden and H. Sharipov, On singularities of the inverse problems associated with perfect cuboids, Arxiv preprint arXiv:1208.1859, 2012.
  72. J. Ramsden and R, Sharipov, On two algebraic parametrizations for rational solutions of the cuboid equations, Arxiv preprint arXiv:1208.2587, 2012
  73. J. Randon-Furling, S. Redner, Residence Time Near an Absorbing Set, arXiv:1806.09028 [cond-mat.stat-mech], 2018. (A000629)
  74. S. V. S. Ranganathan, D. Divsalar, R. D. Wesel, On the Girth of (3, L) Quasi-Cyclic LDPC Codes based on Complete Protographs, arXiv preprint arXiv:1504.04975v2, 2015
  75. Jaime Rangel-Mondragon, Polyominoes and Related Families, The Mathematica Journal, 9:3 (2005), 609-640.
  76. J. Rangel-Mondragon, Selected Themes in Computational Non-Euclidean Geometry: Part 1, The Mathematica Journal 15 (2013); http://www.mathematica-journal.com/data/uploads/2013/07/Rangel-Mondragon_Selected-1.pdf
  77. Mani Ranjbar, WG Macready, L Clark, F Gaitan, Generalized Ramsey numbers through adiabatic quantum optimization, arXiv preprint arXiv:1606.01078, 2016
  78. Rankin, Stuart; Flint, Ortho; Schermann, John, Enumerating the prime alternating knots. II. J. Knot Theory Ramifications 13 (2004), no. 1, 101-149.
  79. B. S. Rao, Heptagonal numbers in the Pell sequence and diophantine equations 2x^2 = y^2(5y-3)^2 +- 2, Fib. Quarterly, 43 (2005), 194-201.
  80. B. S. Rao, Heptagonal numbers in the associated Pell sequence ..., Fib. Quarterly, 43 (2005), 302-306.
  81. Tejas R. Rao, An open source software package for primality testing of numbers of the form p2^n + 1, with no constraints on the relative sizes of p and 2^n, 2018. doi:10.7287/peerj.preprints.27396v1 (A046067)
  82. Mohammed A. Raouf, Fazirulhisyam Hashim, Jiun Terng Liew, Kamal Ali Alezabi, Pseudorandom sequence contention algorithm for IEEE 802.11ah based internet of things network, PLoS ONE (2020) Vol. 15, No. 8, e0237386. doi:10.1371/journal.pone.0237386 (A004146, A052955)
  83. Theophanes E. Raptis, Fractality and Coherent Structures in Satisfiability Problems</a>, 2017. PDF (A000041)
  84. Theophanes E. Raptis, Unitary Cellular Automata and Convolution Algebras, arXiv preprint arXiv:1608.05259, 2016
  85. Theophanes E. Raptis, Finite Information Numbers through the Inductive Combinatorial Hierarchy. arXiv:1805.06301 [physics.gen-ph], 2018. (A000120)
  86. Kilian Raschel, Amélie Trotignon, On walks avoiding a quadrant, arXiv:1807.08610 [math.CO], 2018. (A060898)
  87. M Rasheed, N Clement, A Bhowmick, C Bajaj, Quantifying and Visualizing Uncertainties in Molecular Models, arXiv preprint arXiv:1508.03882, 2015
  88. Muhibur Rasheed, N Clement, A Bhowmick, C Bajaj, Statistical Framework for Uncertainty Quantification in Computational Molecular Modeling, in Proceedings of the 7th ACM International Conference on Bioinformatics, Computational Biology, and Health Informatics, Pages 146-155, Seattle, WA, USA — October 02 - 05, 2016 ACM New York, NY, USA doi:10.1145/2975167.2975182
  89. J. Rasku, T. Karkkainen, P. Hotokka, Solution Space Visualization as a Tool for Vehicle Routing Algorithm Development, Proc. FORS-40, 2013; http://www.fors40.org/wp-content/uploads/2013/01/FORS40_Proceedings_ISBN_978-952-265-436-6.pdf#page=14
  90. Arjun K. Rathie, Gradimir V. Milovanović, and Richard B. Paris, Hypergeometric representations of Gelfond's constant and its generalisations, Serbian Academy of Sciences and Arts (2021). PDF (A039661)
  91. Tejmal Rathore, Higher Length Necklaces from Lower Ones When the Absolute Value of the Difference of Two Adjacent Beads Belongs to a Set of Integers, IETE J. Education (2023). doi:10.1080/09747338.2023.2178529
  92. Rauhut, Holger, Random sampling of sparse trigonometric polynomials. Appl. Comput. Harmon. Anal. 22 (2007), no. 1, 16-42.
  93. Vlady Ravelomanana, the Projet PAI Amadeus Collaboration, The Average Size of Giant Components Between the Double-Jump (2006), arXiv:cs/0607057.
  94. S. Rawat, B. Nautiyal, A. Sah and S. Pundir, Power Summation---A Computer Dimension, International Journal of Computer Applications (0975 - 8887), Volume 58- No.6, November 2012; http://research.ijcaonline.org/volume58/number6/pxc3883496.pdf
  95. Anandaroop Ray, Sam Kaplan, John Washbourne, Uwe Albertin, Low frequency full waveform seismic inversion within a tree based Bayesian framework, in Geophysical Journal International (2018), Vol. 212, Issue 1, pp. 522-542. doi:10.1093/gji/ggx428 See also PDF - "We must mention that an invaluable resource while dealing with integer sequences is the Online Encyclopedia of Integer Sequences".
  96. S. G. Rayaguru and R. K. Davala, Sequence cobalacing and almost cobalancing numbers: A different approach, AIP Conference Proceedings (2023) Vol. 2819, Issue 1. doi:10.1063/5.0137791
  97. S. G. Rayaguru, M. K. Sahukar, G. K. Panda, Markov equation with components of some binary recurrent sequences, Notes on Number Theory and Discrete Mathematics (2020) Vol. 26, No. 3, 149–159. doi:10.7546/nntdm.2020.26.3.149–159 (A002559)
  98. Steven Rayan, Aspects of the topology and combinatorics of Higgs bundle moduli spaces, arXiv:1809.05732 [math.AG], 2018. (A000990, A131868, A145855)
  99. R. C. Read, On general dissections of a polygon, Aequat. Math. 18 (1978), 370-388.
  100. Reading, Nathan, Lattice congruences of the weak order. Order 21 (2004), no. 4, 315-344 (2005).
  101. Reading, Nathan, Lattice congruences, fans and Hopf algebras. J. Combin. Theory Ser. A 110 (2005), no. 2, 237-273.
  102. Reading, Nathan Noncrossing partitions and the shard intersection order. J. Algebraic Combin. 33 (2011), no. 4, 483-530.
  103. Esteban Real, Yao Chen, Mirko Rossini, Connal de Souza, Manav Garg, Akhil Verghese, Moritz Firsching, Quoc V. Le, Ekin Dogus Cubuk, and David H. Park, AutoNumerics-Zero: Automated Discovery of State-of-the-Art Mathematical Functions, arXiv:2312.08472 [cs.NE], 2023.
  104. F. Rebatel and E. Thiel, On dimension partitions in discrete metric spaces, 2012.
  105. Bernardo Recáman, The Bogotá Puzzles, Courier Dover Publications (2020). EBOOK (A003052: p. 88, A046759: p. 77)
  106. D. Recoskie and J. Sawada, The Taming of Two Alley CATs, 2012, http://www.socs.uoguelph.ca/~sawada/papers/alley.pdf
  107. Davide Francesco Redaelli, Francesco Viganò, A Bug’s Identity, The Mathematical Intelligencer (2020). doi:10.1007/s00283-020-09994-w
  108. A. Reddick and Y. Xiong, The search for one as a prime number: from ancient Greece to modern times, Electronic Journal of Undergraduate Mathematics, Volume 16, 1 { 13, 2012.
  109. Reeds, James A.; Fishburn, Peter C. Counting split interval orders. Order 18 (2001), no. 2, 129-135.
  110. Dionisel Y. Regalado, Rodel Azura, An Analytic Approximation to the Density of Twin Primes, Recoletos Multidisciplinary Research Journal (2019) Vol. 6, No. 2. HTML (A001692)
  111. A. Regev, Young tableaux and 1/e, preprint.
  112. A. Regev, Asymptotics of Young tableaux in the strip, the d-sums arXiv:1004.4476
  113. Regev, A.; Identities for the number of standard Young tableaux in some (k,l)-hooks. Sem. Lothar. Combin. 63 (2010), Art. B63c, 8 pp.
  114. A. Regev, Enumerating triangulations by parallel diagonals, Arxiv preprint arXiv:1208.3915, 2012, J. Int. Seq. 15 (2012) #12.8.5
  115. A. Regev, The central component of a triangulation, arXiv preprint arXiv:1210.3349, 2012, and <a href="https://cs.uwaterloo.ca/journals/JIS/VOL16/Regev/regev4.html">J. Int. Seq. 16 (2013) #13.4.1</a>
  116. A. Regev, Remarks on two-eared triangulations, arXiv preprint arXiv:1309.0743, 2013
  117. Alon Regev, Amitai Regev, Doron Zeilberger, Identities in character tables of S_n, arXiv preprint arXiv:1507.03499, 2015
  118. A Regev, D Zeilberger, Surprising Relations Between Sums-Of-Squares of Characters of the Symmetric Group Over Two-Rowed Shapes and Over Hook Shapes, arXiv preprint arXiv:1510.07061, 2015
  119. P. Regner, Phylogenetic Trees: Selected Combinatorial Problems, master thesis, TU Vienna, April 2012.
  120. Julie Rehmeyer, The Pattern Collector; The Encyclopedia of Integer Sequences outgrows its creator
  121. Colin D. Reid, Simon M. Smith, Groups acting on trees with Tits' independence property (P), arXiv:2002.11766 [math.GR], 2020. (A000638)
  122. Fabian S. Reid, The Visual Pattern in the Collatz Conjecture and Proof of No Non-Trivial Cycles, arXiv:2105.07955 [math.GM], 2021. (A001045, A016789, A075677, A329480)
  123. Samuel Reid, On Generalizing a Temporal Formalism for Game Theory to the Asymptotic Combinatorics of S5 Modal Frames, arXiv preprint arXiv:1305.0064, 2013
  124. Daniel Reidenbach, Johannes C. Schneider, Morphically primitive words, Theoretical Computer Science, Volume 410, Issues 21-23, 17 May 2009, Pages 2148-2161.
  125. K. Reihani, K-theory of Furstenberg transformation group C^*-algebras, Arxiv preprint arXiv:1109.4473, 2011.
  126. Sten A. Reijers, A sequence approach to solve the Burgers' equation, arXiv:1903.05916 [math.AP], 2019. We are grateful to the OEIS Foundation Inc. for maintaining an extremely useful online encyclopedia of integer sequences.
  127. Markus Reineke, The use of geometric and quantum group techniques for wild quivers (2003), arXiv:math/0304193.
  128. Reineke, Markus Cohomology of quiver moduli, functional equations, and integrality of Donaldson-Thomas type invariants. Compos. Math. 147 (2011), no. 3, 943-964.
  129. Andreas Reinhart, On orders in quadratic number fields whose set of distances is peculiar, arXiv:2305.09267 [math.NT], 2023. See also On orders in quadratic number fields with unusual sets of distances, Acta Arithmetica (2023). doi:10.4064/aa230515-4-10 (A135735)
  130. Andreas Reinhart, A counterexample to the Pellian equation conjecture of Mordell, arXiv:2402.09827 [math.NT], 2024. (A135735)
  131. Ulrich Reitebuch, Henriette-Sophie Lipschütz, and Konrad Polthier, Visualizing the Kolakoski Sequence, Bridges Conf. Proc.; Math., Art, Music, Architecture, Culture (2023) 481-484. Abstract (A000002, A064353, A071820, A079729, A079730)
  132. Andrew Reiter, On (mod n) spirals, 2014; http://www.cw-complex.com/modNspirals/modNspirals.pdf; also posting to Number Theory Mailing List, Mar 23 2014.
  133. Cliff Reiter, Polygonal Numbers and Fifty One Stars, Lafayette College, Easton, PA (2019). PDF (A000326, A005891)
  134. Jeffrey B. Remmel, Consecutive Up-down Patterns in Up-down Permutations, Electron. J. Combin., 21 (2014), #P3.2.
  135. Jeffrey B. Remmel, JLB Tiefenbruck, Q-analogues of convolutions of Fibonacci numbers, - Australasian Journal of Combinatorics, Volume 64(1) (2016), Pages 166–193.
  136. Jeffrey B. Remmel, S Zheng, Rises in forests of binary shrubs, arXiv preprint arXiv:1611.09018, 2016.
  137. Bin Ren, Shruthi Balakrishna, Youngjoon Jo, Sriram Krishnamoorthy, Kunal Agrawal, Milind Kulkarni, Extracting SIMD Parallelism from Recursive Task-Parallel Programs, ACM Transactions on Parallel Computing (2019) Vol. 6, No. 4, Article No. 24. doi:10.1145/3365663
  138. Qingchun Ren, Ordered Partitions and Drawings of Rooted Plane Trees, arXiv preprint arXiv:1301.6327, 2013
  139. XIAO-ZHI REN and YONG-GAO CHEN. On near-perfect numbers with two distinct prime factors, Bulletin of the Australian Mathematical Society, available on CJO2013. doi:10.1017/S0004972713000178.
  140. Antoine Renard, Michel Rigo, and Markus A. Whiteland, q-Parikh Matrices and q-deformed binomial coefficients of words, arXiv:2402.05657 [cs.FL], 2024. See pp. 3, 12. (A133009 pp. 3, 12)
  141. Gabriel Renault, Jeux combinatoires dans les graphes, Thesis, Dr. of Math. and Informatique, L'Université Bordeaux, 2013; http://www.labri.fr/perso/grenault/manuscript.pdf.
  142. P. Repetowicz, U. Grimm and M. Schreiber, arXiv:cond-mat/9901001 High-temperature expansion for Ising models on quasiperiodic tilings, J. Phys. A: Math. Gen. 32 (1999) 4397-4418.
  143. Lorenzo Repetto, Educational Tasks, Fun, and Informatics, International Conference on Informatics in School: Situation, Evaluation and Perspectives (ISSEP 2020) CEUR Vol. 2755, 13-26. PDF (A010060)
  144. Guillermo Restrepo and Leonardo A. Pachon, Mathematical Aspects of the Periodic Law (2006), arXiv:math.GR/0611410.
  145. C. Reutenauer and M. Robado, On an algebraicity theorem of Kontsevich, FPSAC 2012, Nagoya, Japan DMTCS proc. AR, 2012, 241-248; http://www.math.nagoya-u.ac.jp/fpsac12/download/contributed/dmAR0122.pdf.
  146. Alexander Rezchikov, Vadim Kushnikov, Vladimir Ivaschenko, Aleksey Bogomolov, Leonid Filimonyuk, Olga Dolinina, Ekaterina Kulakova, Konstantin Kachur, The Approach to Provide and Support the Aviation Transportation System Safety Based on Automation Models, In: Silhavy R., Silhavy P., Prokopova Z., Senkerik R., Kominkova Oplatkova Z. (eds) Software Engineering Trends and Techniques in Intelligent Systems. CSOC 2017. Advances in Intelligent Systems and Computing, vol. 575. doi:10.1007/978-3-319-57141-6_26
  147. Hayat Rezgui, A proof of Fortune's conjecture correctness in a particular case, Int'l E-Conf. Young Res. Alg. Num. Theor. (2023). Abstract
  148. B. Reznick, Some new canonical forms for polynomials, Arxiv preprint arXiv:1203.5722, 2012 and Pac. J. Math. 266 (1) (2013) 186-220 doi:10.2140/pjm.2013.266.185
  149. RHODES, JOHN RICHARD, (2012) On the Kernel of the Symbol Map for Multiple Polylogarithms, Durham theses, Durham University. Available at Durham E-Theses Online: http://etheses.dur.ac.uk/3905/
  150. José María Grau Ribas, A New Proof and Extension of the Odds-Theorem, arXiv:1812.09255 [math.PR], 2018. (A106533)
  151. Paolo Emilio Ricci, Logarithmic-Sheffer polynomial sets, Jñānābha (2018) Vol. 48 (1), 111-120. PDF
  152. Paolo Emilio Ricci, Logarithmic-Sheffer polynomials of the second kind, Tbilisi Math. J. (2018) Vol. 11, Issue 3, 95-106. Abstract
  153. Paolo Emilio Ricci, Complex Spirals and Pseudo-Chebyshev Polynomials of Fractional Degree, Symmetry (2018) Vol. 10, No. 12, 671. doi:10.3390/sym10120671 (A016825)
  154. Paolo Emilio Ricci, Differential Equations for Classical and Non-Classical Polynomial Sets: A Survey, Axioms (2019) Vol. 8, No. 2, 50. doi:10.3390/axioms8020050 (A000364)
  155. Paolo Emilio Ricci, Generalized hermite polynomial families, Jñānābha (2019) Vol. 49(1), Article 7, 80-88. Abstract (see 7)
  156. Brian Rice, Primitive prime divisors in polynomial arithmetic dynamics, Integers, El. J. Combin. Number Theory 7 (2007) #A26
  157. C. Richard and U. Grimm, arXiv:math.CO/0302302 On the Entropy and Letter Frequencies of Ternary Square-Free Words], math.CO/0302302, Electron. J. Combin. 11 (2004), no. 1, Research Paper 14, 19 pp.
  158. D. Richards, Coordination and Shared Mental Models, American Journal of Political Science, 45 (2001), 259-76.
  159. Seth Richards-Shubik, Application and Computation of a Flexible Class of Network Formation Models, de Paula, Á., Tamer, E. and Voia, M.-C. (Ed.), The Econometrics of Networks (Advances in Econometrics, Vol. 42), Emerald Publishing Ltd. (2020), 111-142.
  160. Mark Richardson, A Needlessly Complicated and Unhelpful Solution to Ben Ames Williams' Famous Coconuts Problem, The Winnower, 4:e147175.52128 (2016). doi:10.15200/winn.147175.52128
  161. S. L. Richardson Jr, Enumeration of the generalized Catalan numbers, MSc Thesis, West Virginia Univ, 2005
  162. T. M. Richardson, The Reciprocal Pascal Matrix, arXiv preprint arXiv:1405.6315, 2014
  163. T. M. Richardson, The Super Patalan Numbers, arXiv preprint arXiv:1410.5880, 2014
  164. Thomas M. Richardson, The three'R's and the Riordan dual, arXiv preprint arXiv:1609.01193, 2016.
  165. David Richeson, Residue Designs, String Art, and Number Theory, Bridges Conf. Proc.; Math., Art, Music, Architecture, Culture (2023) 365-368. Abstract
  166. L. B. Richmond and J. Shallit, Counting Abelian Squares (2008); arXiv:0807.5028
  167. Gwenaël Richomme, A Characterization of Infinite LSP Words, arXiv:1705.05786 [cs.FL], 2017.
  168. Gwenaël Richomme, Characterization of infinite LSP words and endomorphisms preserving the LSP property, arXiv:1808.02680 [cs.DM], 2018. (A000169)
  169. G. Richomme, K. Saari, L. Q. Zamboni, doi:10.1016/j.aam.2010.01.006 Balance and Abelian complexity of the Tribonacci word, Adv. Appl Math. 45 (2) (2010) 212-231
  170. Richter, Christian. "Tilings of convex polygons by equilateral triangles of many different sizes." Discrete Mathematics 343.3 (2020): 111745.
  171. David Richter, Generic Orthotopes, arXiv:2210.12012 [math.CO], 2022. (A000084)
  172. David Richter, Ehrhart Polynomials of Generic Orthotopes, arXiv:2309.09026 [math.CO], 2023. See p. 11. (A000084)
  173. H. Richter, Analyzing coevolutionary games with dynamic fitness landscapes, arXiv preprint arXiv:1603.06374, 2016
  174. Hendrik Richter, Dynamic landscape models of coevolutionary games, arXiv preprint arXiv:1611.09149, 2016
  175. Lukas Riegler, Simple enumeration formulae related to Alternating Sign Monotone Triangles and standard Young tableaux, Dissertation, Universitat Wien, 2014.
  176. Riera, Constanza; Parker, Matthew G. Generalized bent criteria for Boolean functions. I. IEEE Trans. Inform. Theory 52 (2006), no. 9, 4142-4159.
  177. René Rietz, Optimization of Network Intrusion Detection Processes, 2018. PDF (A008277)
  178. Michel Rigo, Syntactical and automatic properties of sets of polynomials over finite fields, Finite Fields and Their Applications, Volume 14, Issue 1, January 2008, Pages 258-276.
  179. Michel Rigo, Formal Languages, Automata and Numeration Systems, 2 vols. Wiley 2014.
  180. Michel Rigo, Invariant games and non-homogeneous Beatty sequences, Slides of a talk, Journée de Mathématiques Discrètes, 2015; PDF
  181. Michel Rigo, Relations on words, arXiv preprint arXiv:1602.03364, 2016
  182. M. Rigo, P. Salimov, and E. Vandomme, "Some Properties of Abelian Return Words", Journal of Integer Sequences, Vol. 16 (2013), #13.2.5.
  183. Michel Rigo and Manon Stipulanti, Revisiting regular sequences in light of rational base numeration systems, arXiv:2103.16966 [cs.FL], 2021. (A014081, A282717)
  184. Michel Rigo, Manon Stipulanti, and Markus A. Whiteland, Gapped Binomial Complexities in Sequences, Univ. Liège (Belgium 2023). PDF (A011973, A102547)
  185. Salah Eddine Rihane and Alain Togbé, Repdigits as products of consecutive Padovan or Perrin numbers, Arab. J. Math. (2021). doi:10.1007/s40065-021-00317-1 (A000931, A001608, A010785)
  186. Salah Eddine Rihane and Alain Togbé, On the intersection of Padovan, Perrin sequences and Pell, Pell-Lucas sequences, Annales Mathematicae et Informaticae (2021). doi:10.33039/ami.2021.03.014 (A000129, A000931, A001608, A002203)
  187. Salah Eddine Rihane and Alain Togbé, Padovan and Perrin numbers as product of two repdigits, Boletín de la Sociedad Matemática Mexicana (2022) Vol. 28, Art. no. 51 (2022). doi:10.1007/s40590-022-00446-3
  188. Salah Eddine Rihane and A Togbé, k-Fibonacci numbers which are Padovan or Perrin numbers, Indian J. Pure Appl. Math. (2022). doi:10.1007/s13226-022-00276-z
  189. Roberto Rinaldi and Marco Ripà, Optimal cycles enclosing all the nodes of a k-dimensional hypercube, arXiv:2212.11216 [math.CO], 2022. (A007283, A318165)
  190. S. Rinaldi, Succession rules: the whole story, Phd thesis, Università di Firenze, 2002.
  191. C. M. Ringel, The Catalan combinatorics of the hereditary artin algebras, arXiv preprint arXiv:1502.06553, 2015.
  192. Sara Riva, Factorisation of Discrete Dynamical Systems (Factorisation de systèmes dynamiques discrets), Ph.D. Thesis, Univ. Côte d'Azur (France 2023). Abstract (A001372, A005248)
  193. Luis Manuel Rivera, Integer sequences and k-commuting permutations, arXiv:1406.3081
  194. John Riordan, Enumeration of plane trees by branches and endpoints, Journal of Combinatorial Theory, Series A, Volume 19, Issue 2, September 1975, Pages 214-222.
  195. J. Riordan, The blossoming of Schroeder's fourth problem, Acta Math., 137 (1976), 1-16.
  196. J. Riordan, A budget of rhyme scheme counts, pp. 455 - 465 of Second International Conference on Combinatorial Mathematics, New York, April 4-7, 1978. Edited by Allan Gewirtz and Louis V. Quintas. Annals New York Academy of Sciences, 319, 1979.
  197. Gabriel Bravo Rios, Agustin Moreno Cañadas, Dyck Paths in Representation Theory of Algebras, National University of Colombia (2020). PDF (A009766)
  198. Marco Ripà, The n x n x n Points Problem Optimal Solution, viXra:1508.0201, 2015.
  199. Marco Ripà, On the Convergence Speed of Tetration, 2018. PDF (A317824, A317903, A317905)
  200. Marco Ripà, Solving the n1 × n2 × n3 Points Problem for n3 < 6, sPIqr Society, World Intelligence Network (2019). Abstract (A225227)
  201. Marco Ripà, The 3 × 3 × … × 3 Points Problem solution, Notes on Number Theory and Discrete Mathematics (2019) Vol. 25, No. 2, 68-75. doi:10.7546/nntdm.2019.25.2.68-75 (A225227, A261547)
  202. Marco Ripà, On the constant congruence speed of tetration, Notes on Number Theory and Discrete Mathematics (2020) Vol. 26, No. 3, 245-260. doi:10.7546/nntdm.2020.26.3.245-260 (A317824, A317903, A317905)
  203. Marco Ripà, The congruence speed formula, Notes on Number Theory and Discrete Mathematics (2021) Vol. 27, No. 4, 43-61. doi:10.7546/nntdm.2021.27.4.43-61 (A224473, A224474, A290372, A290373, A290374, A290375, A317905, A337392)
  204. Marco Ripà, Minimum-Link Covering Trails for any Hypercubic Lattice, World Intel. Netw. (2022). PDF (A225227, A261547)
  205. Marco Ripa, On some open problems concerning perfect powers, arXiv:2205.10163 [math.GM], May 2022.
  206. Marco Ripà, Metric spaces in chess and international chess pieces graph diameters, arXiv:2311.00016 [math.HO], 2023. (A232007 p. 19, A359740, p. 14)
  207. M. Ripa, E. Dalmasso, Patterns related to the Smarandache circular sequence primality problem, Notes Number Theory Discrete Math. 18, No. 1, 29-48 (2012).
  208. M. Ripa and G. Morelli, Retro-analytical Reasoning IQ tests for the High Range, 2013, http://www.iqsociety.org/general/documents/Retro_analytical_Reasoning_IQ_tests_for_the_High_Range.pdf.
  209. S. M. Ripon, Generalization of a class of logarithmic integrals, Integral Transforms and Special Functions, Vol. 26, #4, 2014; doi:10.1080/10652469.2014.989390
  210. Justin Rising, An Order-Theoretic Perspective on Rank Estimation, 2023. doi:10.13140/RG.2.2.22519.19368 (A000670)
  211. Adrian Riskin, A note on heterogeneous decompositions into spanning trees (2006), arXiv:math/0605398.
  212. Thomas Risse, Least Square Approximation with Zernike Polynomials Using SAGE, http://www.weblearn.hs-bremen.de/risse/papers/SiP27/Zernike.pdf.
  213. Roswitha Rissner, Daniel Windisch, Absolute irreducibility of the binomial polynomials, arXiv:2009.02322 [math.AC], 2020. (A076427)
  214. Katherine A. Ritchey, Computational Topology for Configuration Spaces of Disks in a Torus, Ph. D. Dissertation, The Ohio State University (2019). PDF (A003136)
  215. B. Rittaud, "On the Average Growth of Random Fibonacci Sequences", J. Integer Sequences, Volume 10, 2007, Article 07.2.4.
  216. Benoit Rittaud, Elise Janvresse, Emmanuel Lesigne and Jean-Christophe Novelli, Quand les maths se font discretes, Le Pommier, 2008 (ISBN 978-2-7465-0370-0).
  217. Benoit Rittaud and Laurent Vivier, Circular words and applications, Arxiv preprint arXiv:1108.3618, 2011
  218. Benoit Rittaud and Laurent Vivier, Circular words and three applications: factors of the Fibonacci word, F -adic numbers, and the sequence 1, 5, 16, 45, 121, 320,. . . . Functiones et Approximatio Commentarii Mathematici 47 (2012) no. 2, 207-231 doi:10.7169/facm/2012.47.2.6; http://hal.archives-ouvertes.fr/docs/00/56/63/14/PS/CircularWords.ps.
  219. Carlos Rivera, Puzzle 9. Sum of first k primes is perfect square, The Prime Puzzles and Problems Connection. HTML (A033997)
  220. L. M. Rivera, Integer sequences and k-commuting permutations, arXiv preprint arXiv:1406.3081, 2014; Integers, 15 (2015), #A46.
  221. Luis Manuel Rivera, Some properties of token graphs, Honors Research Projects (2018), 728. PDF. (A085680)
  222. Luis Manuel Rivera and Ana Laura Trujillo-Negrete, Hamiltonicity of token graphs of fan graphs, arXiv:1707.05839 [math.CO], 2017.
  223. G. D. Rizell, J. D. Evans, Exotic spheres and the topology of symplectomorphism groups, J. Topol. 8 (2015) 586-602 doi:10.1112/jtopol/jtv007
  224. Kelly Roach doi:10.1145/1504347.1504371 Solving integrals with the quantum computer algebra system, ACM Commun. Comp. Alg. 42 (3) (2008), in text citation
  225. Robbins, Jakayla R., Enumerating orientations of the free spikes. European J. Combin. 28 (2007), no. 3, 868-875.
  226. Jakayla R. Robbins, Representable orientations of the free spikes, Discrete Mathematics, Volume 308, Issue 22, 28 November 2008, Pages 5174-5183.
  227. Neville Robbins, "On Partition Functions and Divisor Sums", J. Integer Sequences, Volume 5, 2002, Article 02.1.4.
  228. David P. Roberts, "Wild Partitions and Number Theory", J. Integer Sequences, Volume 10, 2007, Article 07.6.6.
  229. D. P. Roberts, A. Venkatesh, Hurwitz monodromy and full number fields, PDF, 2014. Also arXiv:1401:7379, 2014.
  230. G. O. Roberts and J. S. Rosenthal, Small and pseudo-small sets for Markov chains, Stochastic Models 17: 121-145, 2001.
  231. Siobhan Roberts, Genius at Play: The Curious Mind of John Horton Conway, Bloomsbury, NY, 2015.
  232. Siobhan Roberts, How to Build a Search Engine for Mathematics, Nautilus, Oct 22, 2015.
  233. Tom Roberts and Thomas Prellberg, Improving Convergence of Generalised Rosenbluth Sampling for Branched Polymer Models by Uniform Sampling, arXiv:2401.12201 [cond-mat.stat-mech], 2024. (A008303 p. 14, A025266 p. 21, A091894 p. 12)
  234. A. Robertson, D. Saracino and D. Zeilberger, Refined Restricted Permutations, In memory of Rodica Simion, Ann. Comb. 6 (2002), no. 3-4, 427-444.
  235. Sylvester Robins, Certain Series of Integral, Rational, Scalene Triangles, Amer. Math. Monthly, (Jan. 1894) Vol. 1, No. 1, 13-14. See Example I. viewer alsodoi:10.2307/2968647. (A072221)
  236. J. P. Robinson, Some postage stamp 2-bases JIS 12 (2009) 09.1.1
  237. R. W. Robinson, Counting Feynman Diagrams.
  238. Aureliano M. Robles-Pérez and José Carlos Rosales, The Frobenius number for sequences of triangular and tetrahedral numbers, arXiv:1706.04378 [math.NT], 2017.
  239. Tom Roby, (Michael Joseph, James Propp), Dynamical Algebraic Combinatorics and the Homomesy Phenomenon: Toggling, whirling, and Bulgarian solitaire, University of Connecticut (March 26 2019). PDF (A000358)
  240. Tom Roby, Dynamical algebraic combinatorics and homomesy: An action-packed introduction, AlCoVE: an Algebraic Combinatorics Virtual Expedition (2020). PDF (A000358)
  241. L. Rocha and E. V. Pereira Spreafico, A Combinatorial Bijection between Ordered Trees and Lattice Paths, Trends in Comp. Appl. Math. (2023) Vol. 24, No. 3, 427-436. doi:10.5540/tcam.2023.024.03.00427
  242. Rochowicz, John A. Jr. (2015), Harmonic Numbers: Insights, Approximations and Applications, Spreadsheets in Education (eJSiE): Vol. 8: Iss. 2, Article 4; http://epublications.bond.edu.au/ejsie/vol8/iss2/4
  243. José Manuel Rodríguez Caballero, Divisors on overlapped intervals and multiplicative functions, arXiv:1709.09621 [math.NT], 2017.
  244. José Manuel Rodríguez Caballero, Elementary number-theoretical statements proved by Language Theory, arXiv:1709.09617 [math.LO], 2017. (A241561 = A071561)
  245. José Manuel Rodríguez Caballero, Symmetric Dyck Paths and Hooley's Δ-Function, In: Brlek S., Dolce F., Reutenauer C., Vandomme É. (eds) Combinatorics on Words, WORDS 2017, Lecture Notes in Computer Science, vol 10432. doi:10.1007/978-3-319-66396-8_23
  246. José Manuel Rodríguez Caballero, Jordan's Expansion of the Reciprocal of Theta Functions and 2-densely Divisible Numbers, Integers (2020) Vol. 20, Article A2. PDF (A174973)
  247. Ø. J. Rødseth, Enumeration of M-partitions, Discrete Math., 306 (2006), 694-698.
  248. Ø. J. Rødseth, Sloane's box stacking problem, Discrete Math., 306 (2006), 2005-2009.
  249. Ø. J. Rødseth, "Minimal r-Complete Partitions", J. Integer Sequences, Volume 10, 2007, Article 07.8.3.
  250. Ø. J. Rødseth and James A. Sellers, "On a Restricted m-Non-Squashing Partition Function", J. Integer Sequences, Volume 8, 2005, Article 05.5.4.
  251. Ø. J. Rødseth, J. A. Sellers and K. M. Courtright, Arithmetic properties of non-squashing partitions into distinct parts, Ann. Comb. 8 (2004), no. 3, 347-353.
  252. E. L. Roettger and H. C. Williams, Appearance of Primes in Fourth-Order Odd Divisibility Sequences, J. Int. Seq., Vol. 24 (2021), Article 21.7.5. HTML (A005013, A056570, A127595, A215465, A215466, A238536, A238537, A238538)
  253. Roettger, E. L.; Williams, H. C.; Guy, R. K. doi:10.1007/978-1-4614-6642-0_15 Some extensions of the Lucas functions. Springer Proceedings in Mathematics & Statistics 43, 271-311 (2013).
  254. D. G. Rogers, Similarity relations on finite ordered sets, Journal of Combinatorial Theory, Series A, Volume 23, Issue 1, July 1977, Pages 88-98. Erratum, loc. cit., 25 (1978), 95-96.
  255. D. G. Rogers, Pascal triangles, Catalan numbers and renewal arrays, Discrete Math., 22 (1978), 301-310.
  256. D. G. Rogers, Rhyming schemes: Crossings and coverings, Discrete Mathematics, Volume 33, Issue 1, 1981, Pages 67-77.
  257. D. G. Rogers and L. W. Shapiro, Some correspondences involving the Schroeder numbers and relations, in Lect. Notes Math., Vol. 686 (1978), pp. 267-276.
  258. D. G. Rogers and L. W. Shapiro, Deques, trees and lattice paths, in Combinatorial Mathematics, VIII (Geelong, 1980), pp. 293-303, Lecture Notes in Math., 884, Springer, Berlin-New York, 1981.
  259. Baptiste Rognerud, Invitation to quiver representation and Catalan combinatorics, Snapshots of modern mathematics from Oberwolfach (2021) No. 4, see p. 8. doi:10.14760/SNAP-2021-004-EN Actually, if you use the wonderful On-line Encyclopedia of Integer Sequences [8] and enter the sequence 1, 1, 2, 5, you will find a very good candidate for our sequence. At the time of writing this article, there are 2219 registered sequences involving our numbers, so it is only one of at least 2219 good candidates.
  260. Valerie Roitner, The vectorial kernel method for walks with longer steps, arXiv:2008.02240 [math.CO], 2020. (A007317, A090981)
  261. Constanze Roitzheim, David Barnes, and Scott Balchin, N-infinity operads and associahedra, Pacific J. Math. (2021). abstract
  262. Santiago Rojas-Rojas, Camila Muñoz, Edgar Barriga, Pablo Solano, Aldo Delgado, and Carla Hermann-Avigliano, Analytic Evolution for Complex Coupled Tight-Binding Models: Applications to Quantum Light Manipulation, arXiv:2310.12366 [quant-ph], 2023. (A000012, A001519, A011782, A024175, A080937, A124302)
  263. T. Rokicki, doi:10.1007/s00283-009-9105-3, Twenty-two moves suffice for Rubik's Cube, Math. Intell. 32 (1) (2010) 33-40.
  264. N. Rolin, A. Ugolnikova, Tilings by 1x1 and 2x2 squares (2014) RAIRO, Theor. Inform. Appl. 50 (1) (2016) 105-116 doi:https://doi.org/10.1051/ita/2016011
  265. Adam Roman, Igor T. Podolak and Agnieszka Deszynska, On the number of clusterings in a hierarchical classification model with overlapping clusters, SCHEDAE INFORMATICAE VOLUME 20 2011, http://www.wuj.pl/UserFiles/File/Schedae%2020/20_07_RomanPodolakDeszynska.pdf.
  266. Fabio Roman, On certain ratios regarding integer numbers which are both triangulars and squares, arXiv:1703.06701 [math.NT], 2017.
  267. Dan Romik, "Some Formulas for the Central Trinomial and Motzkin Numbers", J. Integer Sequences, Volume 6, 2003, Article 03.2.4.
  268. Dan Romik, The dynamics of Pythagorean triples (2004), arXiv:math/0406512 and Trans. Am. Math. Soc. 360 (11) (2008) 6045-6064.
  269. Dan Romik, On Viazovska's modular form inequalities, arXiv:2303.13427 [math.NT], 2023. (A068466)
  270. Roney-Dougal, Colva M.; Unger, William R. The affine primitive permutation groups of degree less than 1000. J. Symbolic Comput. 35 (2003), no. 4, 421-439.
  271. Feng Rong, A note on the topological classification of complex polynomial differential equations with only centre singularities, Journal of Difference Equations and Applications, Volume 18, Issue 11, 2012; doi:10.1080/10236198.2012.721782
  272. Alexis Roquefeuil, Confluence of quantum K-theory to quantum cohomology for projective spaces, arXiv:1911.00254 [math.AG], 2019. (A013587)
  273. D Rorabaugh, Toward the Combinatorial Limit Theory of Free Words, arXiv preprint arXiv:1509.04372, 2015
  274. Simon Rose, Counting Hyperelliptic curves on Abelian surfaces with Quasi-modular forms, PhD thesis, University of British Columbia (2012)
  275. Jay Rosen, The number of product-weighted lead codes for ballots and its relation to the Ursell functions of the linear Ising model, Journal of Combinatorial Theory, Series A, Volume 20, Issue 3, May 1976, Pages 377-384.
  276. Kenneth H. Rosen (Ed.), Handbook of Discrete and Combinatorial Mathematics CRC Press, 1999
  277. K. Rosen, Elementary Number Theory, Addison-Wesley, 2000. Pages 9 and 620.
  278. Zvi Rosen and Yan X. Zhang, Convex Neural Codes in Dimension 1, arXiv:1702.06907 [math.CO], 2017.
  279. N. A. Rosenberg, Coalescent histories for caterpillar-like families, IEEE/ACM Trans. Comp. Biol. Bioinformat. (2013) Vol. 10, 1253-1262. doi:10.1109/tcbb.2013.123 (A355044)
  280. Noah A. Rosenberg PhD and Donna M. Zulman MD, MS, Measures of care fragmentation: Mathematical insights from population genetics, Health Services Research (2020) Vol. 55, No. 2, 318-327. doi:10.1111/1475-6773.13263 (A000041)
  281. Hjalmar Rosengren, Elliptic pfaffians and solvable lattice models, arXiv preprint arXiv:1605.02915, 2016
  282. A. Roshan, P. H. Jones and C. D. Greenman, An Exact, Time-Independent Approach to Clone Size Distributions in Normal and Mutated Cells, arXiv preprint arXiv:1311.5769, 2013
  283. K. A. Ross, Conjunctive Selection Conditions in Main Memory, Proceedings of the 2002 PODS Conference, June 2002.
  284. Kenneth A Ross, First Digits of Squares and Cubes, Math. Mag. 85 (2012) 36–42. doi:10.4169/math.mag.85.1.36.
  285. K. A. Ross and D. E. Knuth, A Programming and Problem Solving Seminar. Trivia Hunt (Appendix A), Stanford University Technical Report STAN-CS-89-1269, July 1989.
  286. Beat Rossmy, Alexander Wiethoff, COMB - Shape as a Meaningful Element of Interaction, TEI 2019 Proceedings of the Thirteenth International Conference on Tangible, Embedded, and Embodied Interaction, ACM, 287-295. doi:10.1145/3294109.3295646
  287. R. A. Rota, On modeling emergent neocortical complexity with complex adaptive systems, MS Thesis, San Diego State Univ., Fall 2012; http://sdsu-dspace.calstate.edu/bitstream/handle/10211.10/3226/Rota_Robert.pdf?sequence=1
  288. Rotbart, Aviv Generator sets for the alternating group. Sém. Lothar. Combin. 65 (2010/12), Art. B65b, 16 pp.
  289. John D. Roth, David A. Garren, and R. Clark Robertson, Integer Carrier Frequency Offset Estimation in OFDM with Zadoff-Chu Sequences, IEEE Int'l Conference on Acoustics, Speech and Signal Processing (ICASSP 2021) 4850-4854. doi:10.1109/ICASSP39728.2021.9413937 (A002378)
  290. Marcello Rotondo and Shin'ichi Nojiri, A toy model of discretized gravity in two dimensions and its extensions, Modern Physics Letters A, 32, 1750149 (2017). doi:10.1142/S0217732317501498, preprint: arXiv:1703.06374 [hep-th], 2017.
  291. Ori Rottenstreich, Yossi Kanizo, Haim Kaplan, Jennifer Rexford, Accurate Traffic Splitting on Commodity Switches, SPAA '18: Proceedings of the 30th Symposium on Parallelism in Algorithms and Architectures, 311-320. doi:10.1145/3210377.3210412, PDF. Also IEEE Journal on Selected Areas in Communications (2018) Vol. 36, Issue 10, 2190-2201. HTML, also PDF
  292. Matthew Roughan, Surreal Birthdays and Their Arithmetic, arXiv:1810.10373 [math.HO], 2018. (A007018, A047662, A047665)
  293. Matthew Roughan, The Polylogarithm Function in Julia, arXiv:2010.09860 [math.NA], 2020. (A027642)
  294. Xavier Roulleau, On the dynamics of the line operator Λ{{2},{3}} on some arrangements of six lines, arXiv:2306.01052 [math.CO], 2023. (A001045)
  295. Tomáš Roun, Graph Database Fundamental Services, BS Thesis, Czech Technical University in Prague, 2018. PDF (A000088)
  296. A. Rovenchak, Enumeration of plane partitions with a restricted number of parts, arXiv preprint arXiv:1401.4367, 2014
  297. JT Rowell, Solution Sequences for the Keyboard Problem and its Generalizations, Journal of Integer Sequences, 18 (2015), #15.10.7.
  298. Eric S. Rowland, A simple prime-generating recurrence (2007), arXiv:0710.3217.
  299. Eric S. Rowland, A natural prime-generating recurrence, JIS 11 (2008) 08.2.8
  300. Eric S. Rowland, doi:10.1016/j.jcta.2010.03.004, Pattern avoidance in binary trees, J. Comb. Theory A 117 (6) (2010) 741-758
  301. Eric Rowland, Bell numbers modulo 8, in Combinatorics and Algorithmics of Strings, 2014, page 42; PDF
  302. Eric Rowland, A matrix generalization of a theorem of Fine, arXiv:1704.05872 [math.NT], 2017.
  303. Eric Rowland, Binomial Coefficients, Valuations, and Words, In: Charlier É., Leroy J., Rigo M. (eds) Developments in Language Theory, DLT 2017, Lecture Notes in Computer Science, vol 10396. doi:10.1007/978-3-319-62809-7_3
  304. Eric Rowland, A matrix generalization of a theorem of Fine, Integers (2018) 18A, Article #A18. Abstract (A106407)
  305. Eric Rowland, INTEGERSEQUENCES: A Package for Computing with k-Regular Sequences, International Congress on Mathematical Software (ICMS 2018): Mathematical Software, Lecture Notes in Computer Science (LNCS) Vol. 10931, 414-421. doi:10.1007/978-3-319-96418-8_49
  306. E. Rowland, R. Yassawi, Automatic congruences for diagonals of rational functions, arXiv preprint arXiv:1310.8635, 2013
  307. E. Rowland, D. Zeilberger, A Case Study in Meta-AUTOMATION: AUTOMATIC Generation of Congruence AUTOMATA For Combinatorial Sequences, arXiv preprint arXiv:1311.4776, 2013
  308. Daniel A Rowlands, A Lamacraft, Noisy Spins and the Richardson-Gaudin Model, arXiv preprint arXiv:1711.00828, 2017.
  309. Souvik Roy, Nazim Fatès, and Sukanta Das, Reversibility of Elementary Cellular Automata with fully asynchronous updating: an analysis of the rules with partial recurrence, hal-04456320 [nlin.CG], [cs], 2024. Abstract (A000032, A001609, A001644, A072328, A182097)

(A000032 p. 14, A001609 p. 19, A001644 p. 17, A072328 p. 17, A182097 p. 17)

  1. Gordon F. Royle, "Counting Set Covers and Split Graphs", J. Integer Sequences, Volume 3, 2000, Article 00.2.6.
  2. Gordon F. Royle, Cheryl E. Praeger, S. P. Glasby, Saul D. Freedman, and Alice Devillers, Tournaments and Even Graphs are Equinumerous, arXiv:2204.01947 [math.CO], 2022. (A000568)
  3. Leonard Rozendaal, Pisano word, tesselation, plane-filling fractal, Preprint, 2017.
  4. Suthee Ruangwises, The Landscape of Computing Symmetric n-Variable Functions with 2n Cards, arXiv:2306.13551 [cs.CR], 2023. (A005418)
  5. Martin Rubey, Extended Rate, more GFUN (2007), arXiv:math/0702086.
  6. Martin Rubey, Nestings of Matchings and Permutations and North Steps in PDSAWs (2007); arXiv:0712.2804
  7. Rubey, Martin The number of ribbon Schur functions. Sém. Lothar. Combin. 64 (2010/11), Art. B64c, 11 pp.
  8. Martin Rubey and Christian Stump, Double deficiencies of Dyck paths via the Billey-Jockusch-Stanley bijection, arXiv:1708.05092 [math.CO], 2017.
  9. Martin Rubey, Christian Stump, FindStat – a database and search engine for combinatorial statistics and maps, Proceedings of the 31st Conference on Formal Power Series and Algebraic Combinatorics (Ljubljana), Séminaire Lotharingien de Combinatoire (2019) Vol. 82B, Article #103. PDF (A008292) The On-Line Encyclopedia of Integer Sequences OEIS is an incredibly valuable tool in mathematical research. As a ‘fingerprint database for theorems’ it allows to identify interconnections and relations between theorems throughout mathematics. In this spirit, FindStat is a collaborative online database of combinatorial statistics on combinatorial collections and of combinatorial maps between such collections.
  10. Noah Rubin, Curtis Bright, Kevin K. H. Cheung, and Brett Stevens, Integer and Constraint Programming Revisited for Mutually Orthogonal Latin Squares, arXiv:2103.11018 [cs.DM], 2021. (A000315, A002865)
  11. Noah Rubin, Curtis Bright, Brett Stevens, and Kevin Cheung, IP and CP Revisited for Mutually Orthogonal Latin Squares (Student Abstract), Carleton University (Ottawa, Canada 2022). PDF (A002865)
  12. M. Rubinchik, A. M. Shur, Eertree: An Efficient Data Structure for Processing Palindromes in Strings, arXiv preprint arXiv:1506.04862, 2015
  13. M. O. Rubinstein, Identities for the Rieman zeta function, Ramanujan J. 27, No. 1, 29-42 (2012). doi:10.1007/s11139-010-9276-8 arXiv:0812.2592
  14. Michelle Rudolph-Lilith, On the Product Representation of Number Sequences, with Application to the Fibonacci Family, arXiv preprint arXiv:1508.07894, 2015
  15. M. Rudolph-Lilith, L. E. Muller, On an explicit representation of central (2k+1)-nomial coefficients, arXiv preprint arXiv:1403.5942, 2014
  16. Rudolph-Lilith, Michelle, and Lyle E. Muller, On a link between Dirichlet kernels and central multinomial coefficients, Discrete Mathematics 338.9 (2015): 1567-1572, doi:10.1016/j.disc.2015.04.001.
  17. Pornrat Ruengrot and Duangkamon Baowan, Classification of k-defect holes on a graphene sheet, Comp. Materials Sci. (2023) Vol. 225, 112181. doi:10.1016/j.commatsci.2023.112181 (A258017)
  18. Helmut Ruhland, Somos-4 and a quartic Surface in ℝℙ³, arXiv:2312.02085 [math.AG], 2023. (A006720, A006769, A051138)
  19. Carlos Alexis Gómez Ruiz and Florian Luca, Fibonacci factoriangular numbers, Indagationes Mathematicae, Volume 28, Issue 4, August 2017, p. 796-804. doi:10.1016/j.indag.2017.05.002
  20. Sebastiam M. Ruiz, Comments about the Euclid's proof by reduction to the absurd of the infinitude of prime numbers, 2017; https://www.researchgate.net/profile/Sebastian_Martin_Ruiz/publication/279173567_PrimeNumbersEuclidesMartinRuiz/links/558ad83f08ae31beb100353f/PrimeNumbersEuclidesMartinRuiz.pdf
  21. Josef Rukavicka, On Number of Rich Words, arXiv:1701.07778 [math.CO], 2017.
  22. Josef Rukavicka, An Upper Bound for Palindromic and Factor Complexity of Rich Words, arXiv:1810.03573 [math.CO], 2018. (A216264)
  23. Josef Rukavicka, Secretary problem and two almost the same consecutive applicants, arXiv:2106.11244 [math.PR], 2021. (A002464)
  24. Susanna E. Rumsey, Stark C. Draper, and Frank R. Kschischang, Information Density in Multi-Layer Resistive Memories, IEEE Transactions on Information Theory (2020) Vol. 67, Issue 3, 1446-1460. doi:10.1109/TIT.2020.3040255 (A014235)
  25. Frank Ruskey and Chris Deugau, The combinatorics of certain k-ary meta-Fibonacci sequences, J. Int. Sequenc. 12 (2009) #09.4.3
  26. Frank Ruskey, C. R. Miers and J. Sawada, The number of irreducible polynomials and Lyndon words with given trace, SIAM J. Discrete Math., 14 (2001) 240-245.
  27. Frank Ruskey and Mark Weston, Spherical Venn Diagrams with Involutory Isometries, Electronic Journal of Combinatorics, 18 (2011), #P191; http://www.combinatorics.org/Volume_18/PDF/v18i1p191.pdf
  28. Frank Ruskey and Aaron Williams, An explicit universal cycle for the (n-1)-permutations of an n-set (2007), arXiv:0710.1842.
  29. Frank Ruskey and Aaron Williams, doi:10.1145/1798596.1798598 An explicit universal cycle for the (n-1)-permutations of an n-set, ACM Trans. Algor. 6 (3) (2010) # 45
  30. Ruskey, Frank; Williams, Aaron The feline Josephus problem. Theory Comput. Syst. 50 (2012), no. 1, 20-34.
  31. Frank Ruskey and J. Woodcock, Counting Fixed-Height Tatami Tilings, Electronic Journal of Combinatorics, Paper R126 (2009) 20 pages.
  32. Frank Ruskey and Jennifer Woodcock, The Rand and block distances of pairs of set partitions, in International Workshop on Combinatorial Algorithms, Victoria, LNCS 7056 (2011) p 287 -299 doi:10.1007/978-3-642-25011-8_23
  33. Frank Ruskey, Jennifer Woodcock and Yuji Yamauchi, Counting and computing the Rand and block distances of pairs of set partitions, Journal of Discrete Algorithms, Volume 16, October 2012, Pages 236-248.
  34. Matthew Christopher Russell, Using experimental mathematics to conjecture and prove theorems in the theory of partitions and commutative and non-commutative recurrences, PhD Dissertation, Mathematics Department, Rutgers University, May 2016; http://www.math.rutgers.edu/~zeilberg/Theses/MatthewRussellThesis.pdf.
  35. Felice Russo, An experimental evidence on the validity of third Smarandache conjecture, HTML (A038458).
  36. Luís M. S. Russo, Ana D. Correia, Gonzalo Navarro, Alexandre P. Francisco, Approximating Optimal Bidirectional Macro Schemes, arXiv:2003.02336 [cs.DS], 2020. (A005942)
  37. Vincent Russo and Loren Schwiebert, Beatty sequences, Fibonacci numbers and the golden ratio, http://www-personal.umich.edu/~vprusso/Fibonacci.pdf
  38. John S. Rutherford, Sublattice enumeration. IV. Equivalence classes of plane sublattices by parent Patterson symmetry and colour lattice group type, Acta Cryst. (2009). A65, 156163.
  39. Jan Rutten, The Method of Coalgebra: exercises in coinduction, 2018. PDF (A000045, A000108, A000110, A000166, A006318)
  40. Ruzhansky, Michael; Turunen, Ville; Wirth, Jens doi:10.1007/s00041-014-9322-9 Hörmander class of pseudo-differential operators on compact Lie groups and global hypoellipticity. J. Fourier Anal. Appl. 20, No. 3, 476-499 (2014).
  41. Giulio Ruzza and Di Yang, On the spectral problem of the quantum KdV hierarchy, arXiv:2104.01480 [math-ph], 2021. (A238641)
  42. A. Ryabov, P. Chvosta, Tracer dynamics in a single-file system with absorbing boundary, arXiv preprint arXiv:1402.1949, 2014
  43. David Ryan, Mathematical Harmony Analysis, arXiv preprint arXiv:1603.08904, 2016
  44. David Ryan, An algorithm to assign musical prime commas to every prime number and construct a universal and compact free Just Intonation musical notation, arXiv:1612.01860 [cs.SD], 2017.
  45. Nathan C Ryan, The Height of Divisors of x^n-1 (A114536)
  46. Kevin Ryde, Iterations of the Dragon Curve, Preprint, February 2021; https://download.tuxfamily.org/user42/dragon/dragon.pdf [See A-number index, mentions A000007, A000120, A000265, A000749, A000975, A001045, A001622, A001787, A001792, A003188, A003230, A003476, A003477, A003478, A003479, A004277, A005428, A005578, A005811, A007400, A007404, A007910, A007949, A014176, A014577, A014985, A016029, A020775, A020797, A020829, A021039, A021067, A021913, A021949, A023105, A027383, A029744, A029837, A030300, A034947, A036987, A038189, A038503, A038504, A038505, A043724, A043725, A043726, A043727, A046980, A047617, A051032, A052537, A052953, A052955, A056830, A057744, A060236, A060833, A060961, A061418, A061419, A061420, A061776, A062092, A063920, A066321, A066323, A070875, A077870, A077949, A077950, A077957, A083286, A083658, A086445, A087088, A088431, A088742, A090678, A091067, A091072, A094214, A094874, A102525, A105531, A106836, A106838, A106841, A112030, A112658, A115451, A116178, A118831, A122002, A123208, A125047, A131056, A131078, A135318, A136013, A136408, A137426, A143347, A146559, A154252, A155803, A156595, A164395, A168596, A171476, A171977, A173318, A177057, A178420, A189706, A189715, A189716, A195693, A195727, A203175, A205083, A227036, A228693, A241892, A246960, A253786, A255068, A255070, A256441, A260482, A260747, A260748, A260749, A260750, A268411, A272031, A275975, A289265, A290884, A290885, A293506, A318438, A318439, A332383, A332384, A340669, A340670]
  47. Maria Ryskina and Kevin Knight, Learning Mathematical Properties of Integers, arXiv:2109.07230 [cs.CL], 2021.
  48. G. Rządkowski, Two formulas for Successive Derivatives and Their Applications, JIS 12 (2009) 09.8.2
  49. Grzegorz Rządkowski, M Urlińska, A Generalization of the Eulerian Numbers- arXiv preprint arXiv:1612.06635, 2016.
  50. Grzegorz Rządkowski, Małgorzata Urlińska, Some applications of the generalized Eulerian numbers, Journal of Combinatorial Theory, Series A (2019) Vol. 163, 85-97. doi:10.1016/j.jcta.2018.11.012

About this page

  • This is part of the series of OEIS Wiki pages that list works citing the OEIS.
  • Additions to these pages are welcomed.
  • But if you add anything to these pages, please be very careful — remember that this is a scientific database. Spell authors' names, titles of papers, journal names, volume and page numbers, etc., carefully, and preserve the alphabetical ordering.
  • If you are unclear about what to do, contact one of the Editors-in-Chief before proceeding.
  • Works are arranged in alphabetical order by author's last name.
  • Works with the same set of authors are arranged by date, starting with the oldest.
  • The full list of sections is: A Ba Bi Ca Ci D E F G H I J K L M N O P Q R Sa Sl T U V W X Y Z.
  • For further information, see the main page for Works Citing OEIS.