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"This paper contains several proofs of identities that we first conjectured on the basis of numerical investigation, hugely facilitated by access to Sloane's wonderful sequence finder." [David H. Bailey et al., 2008]

"This note makes reference to many sequences to be found in the OEIS, which at the time of writing contains more than 300,000 sequences. All who work in the area of integer sequences are profoundly indebted to Neil Sloane. Many of the sequences in this note are related to simplicial objects such as the associahedron and the permutahedron. Indeed, the T-transform provides an enumerative link between these two objects, while the P pipeline brings these two objects back to more basic objects. The comments of Tom Copeland and Peter Bala in the relevant OEIS entries have been very useful in this context." [Paul Barry, 2018]

"We have guessed (2.21) with the help of OEIS ." [Connor Behan, 2017]

"The OEIS is the oldest mathematical database, and arguably the most influential one." [Katja Berčič, 2019]

"The On-Line Encyclopedia of Integer Sequences [6] told him that the determinants of these matrices were given by sequence A079340, and a conjectured formula could be found there." [Gaurav Bhatnagar and Christian Krattenthaler, 2017]

"We found the formulas for the coefficients in Proposition 11 thanks to OEIS database." [Stefan Barańczuk, 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.
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  • 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 Ba to Bh.
  • 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.
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  1. E. Baake, M. Baake, M. Salamat, The general recombination equation in continuous time and its solution, arXiv preprint arXiv:1409.1378, 2014
  2. Michael Baake and Michael Coons, A natural probability measure derived from Stern's diatomic sequence, arXiv:1706.00187 [math.NT], 2017.
  3. M. Baake, F. Gahler and U. Grimm, Examples of substitution systems and their factors, arXiv preprint arXiv:1211.5466, 2012; Journal of Integer Sequences, Vol. 16 (2013), #13.2.14.
  4. M. Baake and U. Grimm, arXiv:cond-mat/9706122 Coordination sequences for root lattices and related graphs, Zeit. f. Kristallographie, 212 (1997), 253-256.
  5. Michael Baake, Uwe Grimm, Fourier transform of Rauzy fractals and point spectrum of 1D Pisot inflation tilings, arXiv:1907.11012 [math.MG], 2019. (A106273)
  6. Michael Baake, Uwe Grimm, Manuela Heuer et al., Coincidence rotations of the root lattice A_4 (2007), arXiv:0709.1341; European Journal of Combinatorics, Volume 29, Issue 8, November 2008, Pages 1808-1819.
  7. M. Baake, U. Grimm, J. Nilsson, Scaling of the Thue-Morse diffraction measure, arXiv preprint arXiv:1311.4371, 2013
  8. Michael Baake, Manuela Heuer, Robert V. Moody, Similar sublattices of the root lattice A_4 (2007), arXiv:math/0702448; Journal of Algebra, Volume 320, Issue 4, 15 August 2008, Pages 1391-1408.
  9. M. Baake and R. V. Moody, Similarity submodules and root systems in four dimensions, Canadian Journal of Mathematics (1999), Vol 51 No 6, pp. 1258-1276.
  10. Michael Baake and Natascha Neumaerker, A note on the relation between fixed point and orbit count sequences (2008) arXiv:0812.4354 and JIS 12 (2009) 09.4.4.
  11. Michael Baake, Natascha Neumarker and John A. G. Roberts, ORBIT STRUCTURE AND (REVERSING) SYMMETRIES OF TORAL ENDOMORPHISMS ON RATIONAL LATTICES, PDF, Discrete Contin. Dyn. Syst. 33, No. 2, 527-553 (2013) doi:
  12. Michael Baake, John A. G. Roberts, Alfred Weiss, Periodic orbits of linear endomorphisms on the 2-torus and its lattices (2008); arXiv:0808.3489
  13. Nils A. Baas, A Stacey, Investigations of Higher Order Links, arXiv preprint arXiv:1602.06450, 2016
  14. L. Babai and P. J. Cameron, Automorphisms and enumeration of switching classes of tournaments, The Electronic Journal of Combinatorics, Volume 7(1), 2000, R#38.
  15. B. Babcock, Revisiting the spreading and covering numbers, arXiv:1109.5847, 2011
  16. Babcock, Ben; Van Tuyl, Adam Revisiting the spreading and covering numbers. Australas. J. Combin. 56 (2013), 77-84.
  17. Martin Bača, Susana-Clara López, Francesc-Antoni Muntaner-Batle, Andrea Semaničová-Feňovčíková, The n-queens problem: a new approach, arXiv:1703.09942 [math.CO], 2017.
  18. M. Bača, S. C. López , F. A. Muntaner-Batle, A. Semaničová-Feňovčíková, New Constructions for the n-Queens Problem, Results in Mathematics (2020) Vol. 75, Article No. 41. doi:10.1007/s00025-020-1166-9
  19. Silvia Bacchelli, Luca Ferrari, Renzo Pinzani et al., Mixed succession rules: the commutative case (2008); arXiv:0806.0799 and J. Comb. Theory A 117 (5) (2010) 568-582 doi:10.1016/j.jcta.2009.11.005
  20. Eric Bach and Lev Borisov, Absorption Probabilities for the Two-Barrier Quantum Walk (2009) arXiv:0901.4349
  21. Eric Bach, Jeremie Dusart, Lisa Hellerstein, Devorah Kletenik, Submodular Goal Value of Boolean Functions, arXiv:1702.04067 [cs.DM], 2017.
  22. E Bach, R Fernando, Infinitely Many Carmichael Numbers for a Modified Miller-Rabin Prime Test, arXiv preprint arXiv:1512.00444, 2015
  23. QT Bach, R Paudyal, JB Remmel, A Fibonacci analogue of Stirling numbers, arXiv preprint arXiv:1510.04310, 2015
  24. Quang T. Bach, Roshil Paudyal, Jeffrey B. Remmel, Q-analogues of the Fibo-Stirling numbers, arXiv:1701.07515, 2017
  25. QT Bach, JB Remmel, Generating functions for descents over permutations which avoid sets of consecutive patterns, arXiv preprint arXiv:1510.04319, 2015
  26. QT Bach, JB Remmel, Descent c-Wilf Equivalence, arXiv preprint arXiv:1510.07190, 2015
  27. A. Bacher, Directed and multi-directed animals on the square lattice with next nearest neighbor edges, arXiv preprint arXiv:1301.1365, 2013
  28. Axel Bacher, Improving the Florentine algorithms: recovering algorithms for Motzkin and Schröder paths, arXiv:1802.06030 [cs.DS], 2018. (A000108, A001003, A001006, A001405, A005773, A006318, A026003, A247623)
  29. Bacher, Axel; Bernini, Antonio; Ferrari, Luca; Gunby, Benjamin; Pinzani, Renzo; West, Julian. The Dyck pattern poset. Discrete Math. 321 (2014), 12--23. MR3154009.
  30. Axel Bacher, O Bodini, HK Hwang, TH Tsai, Generating random permutations by coin-tossing: classical algorithms, new analysis and modern implementation, preprint, 2016;
  31. Roland Bacher, Fair Triangulations (2007), arXiv:0710.0960.
  32. Roland Bacher, On generating series of complementary planar trees (2004), arXiv:math/0409050.
  33. R. Bacher, Twisting the Stern sequence, arXiv:1005.5627
  34. Roland Bacher, Counting Packings of Generic Subsets in Finite Groups, Electr. J. Combinatorics, 19 (2012), #P7.
  35. Roland Bacher, Counting invertible Schrodinger Operators over Finite Fields for Trees, Cycles and Complete Graphs, preprint, 2015.
  36. R Bacher, Chebyshev polynomials, quadratic surds and a variation of Pascal's triangle, arXiv preprint arXiv:1509.09054, 2015
  37. Roland Bacher, On the number of perfect lattices, 2017. hal-01503749v1; (only version 1 refers to the OEIS)
  38. Roland Bacher, P De La Harpe, Conjugacy growth series of some infinitely generated groups. 2016. hal-01285685v2;
  39. Roland Bacher and Philippe Flajolet, Pseudo-factorials, elliptic functions, and continued fractions (2009) arXiv:0901.1379 and Ramanujan J. 21 (1) (2010) 71-97
  40. R. Bacher and D. Garber, arXiv:math.GT/0205245 Spindle configurations of skew lines, Geom. Topol. 11 (2007), 1049-1081.
  41. Bacher, R.; Krattenthaler, C. Chromatic statistics for triangulations and Fuß-Catalan complexes. Electron. J. Combin. 18 (2011), no. 1, Paper 152, 16 pp.
  42. R. Bacher, C. Reutenauer, The number of right ideals of given codimension over a finite field, in Noncommutative Birational Geometry, Representations and Combinatorics, edited by Arkady. Berenstein and Vladimir. Retakha, Contemporary Mathematics, Vol. 592, 2013.
  43. R Bacher, C Reutenauer, Number of right ideals and a q-analogue of indecomposable permutations, arXiv preprint arXiv:1511.00426, 2015
  44. Bacher, Roland and Schaeffer, Gilles, On generating series of coloured planar trees. Sém. Lothar. Combin. 55 (2005/06), Art. B55e, 20 pp.
  45. R. Bacher and C. Krattenthaler, Chromatic statistics for triangulations and FussCatalan complexes, Electronic Journal of Combinatorics, 18 (2011), #P152.
  46. J Backelin, Sizes of the extremal girth 5 graphs of orders from 40 to 49, arXiv preprint arXiv:1511.08128, 2015
  47. R. Backhouse, J. F. Ferreira. On Euclid’s algorithm and elementary number theory. Sci. Comput. Program. 76, No. 3, 160-180 (2011). doi:10.1016/j.scico.2010.05.006
  48. Dave Bacon, Andrew M. Childs, Wim van Dam, Optimal measurements for the dihedral hidden subgroup problem (2005), arXiv:quant-ph/0501044.
  49. D. Baczkowski, J. Eitner, C. E. Finch, B. Suminski, M. Kozek, Polygonal, Sierpinski, and Riesel numbers, Journal of Integer, 2015 Vol 18. #15.8.1.
  50. Tej Bade, Kelly Cui, Antoine Labelle, Deyuan Li, Ulam Sets in New Settings, arXiv:2008.02762 [math.CO], 2020. See also Integers (2020) Vol. 20, #A102. PDF (A046932)
  51. C. Badea, On some criteria of irrationality for series of positive rationals : a survey, in Actes de rencontres Arithmetiques de Caen (a la memoire de Roger Apery), 2-3 juin 1995, 1-14.
  52. IVAN BADINSKKI, CHRISTOPHER HUFFAKER, NATHAN MCCUE, CAMERON N. MILLER, KAYLA S. MILLER, STEVEN J. MILLER, AND MICHAEL STONE, The M&M Game: From Morsels to Modern Mathematics, arXiv preprint arXiv:1508.06542, 2015
  53. Dzmitry Badziahin, Jeffrey Shallit, An Unusual Continued Fraction, preprint arXiv:1505.00667, 2015 (A006519, A100338, A100865, A100864)
  54. Sunghan Bae, Su Hu, Min Sha, On the Carmichael rings, Carmichael ideals and Carmichael polynomials, arXiv:1809.05432 [math.NT], 2018. (A002997)
  55. HUNKI BAEK, SEJEONG BANG, DONGSEOK KIM, AND JAEUN LEE, A bijection between aperiodic palindromes and connected circulant graphs, arXiv:1412.2426, 2014
  56. Arpan Bagchi, Encoding and avoiding 2-connected patterns in polygon dissections and outerplanar graphs, J. Phys.: Conf. Ser. 965 012007 (2018). doi:10.1088/1742-6596/965/1/012007 (A001006)
  57. O. Bagdasar, On some functions involving the lcm and gcd of integer tuples, SCIENTIFIC PUBLICATIONS OF THE STATE UNIVERSITY OF NOVI PAZAR, SER. A: APPL. MATH. INFORM. AND MECH. vol. 1, 1 2014. [Another reference gives a different volume number: SER. A: APPL. MATH. INFORM. AND MECH. vol. 6, 2 (2014), 91-100.]
  58. O. Bagdasar, On certain computational and geometric properties of complex Horadam orbits, ANTS 2014,
  59. Ovidiu Bagdasar and Dorin Andrica, New results and conjectures on 2-partitions of multisets, 2017 7th International Conference on Modeling, Simulation, and Applied Optimization (ICMSAO). doi:10.1109/ICMSAO.2017.7934928
  60. Ovidiu Bagdasar, Dorin Andrica, A new formula for the coefficients of Gaussian polynomials, Analele Stiintifice ale Universitatii Ovidius Constanta (2019). Abstract
  61. Ovidiu Bagdasar, Eve Hedderwick, Ioan-Lucian Popa, On the ratios and geometric boundaries of complex Horadam sequences, Electronic Notes in Discrete Mathematics (2018) Vol. 67, 63-70. doi:10.1016/j.endm.2018.05.011 (A000032, A000045, A000129)
  62. O. D. Bagdasar and P. J. Larcombe, On the number of complex Horodam sequences ..., Fib. Q., 51 (2013), 339-347.
  63. Ovidiu D. Bagdasar and Larcombe, Peter J., "On the masked periodicity of Horadam sequences: a generator-based approach", Fib. Q., 55 (2017), 332-339
  64. Ovidiu Bagdasar, I.-L. Popa, On the geometry of certain periodic non-homogeneous Horadam sequences, Electronic Notes in Discrete Mathematics 56 (2016) 7–13; doi:10.1016/j.endm.2016.11.002
  65. Ovidiu Bagdasar, Ralph Tatt, On some new arithmetic functions involving prime divisors and perfect powers, Electronic Notes in Discrete Mathematics (2018) Vol. 70, 9-15. doi:10.1016/j.endm.2018.11.002 (A303748)
  66. Armen G. Bagdasaryan, Ovidiu Bagdasar, On some results concerning generalized arithmetic triangles, Electronic Notes in Discrete Mathematics (2018) Vol. 67, 71-77. doi:10.1016/j.endm.2018.05.012 (A001405, A002426, A005191, A005581, A005712, A007318, A008287, A027907, A035343)
  67. Armen G. Bagdasaryan, Ovidiu Bagdasar, On an arithmetic triangle of numbers arising from inverses of analytic functions, Electronic Notes in Discrete Mathematics (2018) Vol. 70, 17-24. doi:10.1016/j.endm.2018.11.003
  68. Marco Baggio, Vasilis Niarchos, Kyriakos Papadodimas, Gideon Vos, Large-N correlation functions in N = 2 superconformal QCD, arXiv preprint arXiv:1610.07612, 2016
  69. Aaron R. Bagheri, Classifying the Jacobian Groups of Adinkras, (2017), HMC Senior Theses.
  70. Fatemeh Bagherzadeh and Murray Bremner, Commutativity in double interchange semigroups, arXiv:1706.04693 [math.RA], 2017.
  71. Fatemeh Bagherzadeh, M Bremner, S Madariaga, Jordan Trialgebras and Post-Jordan Algebras, arXiv preprint arXiv:1611.01214, 2016.
  72. Eli Bagno, Riccardo Biagioli, David Garber, Some identities involving second kind Stirling numbers of types B and D, arXiv:1901.07830 [math.CO], 2019. (A039755, A039760, A143395)
  73. Eli Bagno, Estrella Eisenberg, Shulamit Reches, Moriah Sigron, On the poset of King-Non-Attacking permutations, arXiv:1905.02387 [math.CO], 2019. (A002464)
  74. Eli Bagno, Estrella Eisenberg, Shulamit Reches, Moriah Sigron, Separators - a new statistic for permutations, arXiv:1905.12364 [math.CO], 2019. (A137774)
  75. Eli Bagno, Estrella Eisenberg, Shulamit Reches, Moriah Sigron, Counting King Permutations on the Cylinder, arXiv:2001.02948 [math.CO], 2020. (A002464, A002493)
  76. Eli Bagno, David Garber, Signed partitions - A balls into urns approach, arXiv:1903.02877 [math.CO], 2019. (A039755, A143395)
  77. Eli Bagno, David Garber, Mordechai Novick, The Worpitzky identity for the groups of signed and even-signed permutations, arXiv:2004.03681 [math.CO], 2020. (A060187, A262226)
  78. Connor Behan, Conformal manifolds: ODEs from OPEs, arXiv preprint arXiv:1709.03967, 2017. [“We have guessed (2.21) with the help of OEIS [38]. However, a proof should be possible with the technology of [39].”]
  79. Maryam Bahrani and Jérémie Lumbroso, Enumerations, Forbidden Subgraph Characterizations, and the Split-Decomposition, arXiv:1608.01465, 2016.
  80. Sen Bai, X Bai, X Che, X Wei, Maximal Independent Sets in Heterogeneous Wireless Ad Hoc Networks, IEEE Transactions on Mobile Computing (Volume: 15, Issue: 8, Aug. 1 2016), 2023 - 2033
  81. Alex Bailey, Martin Finn-Sell, Robert Snocken, Subsemigroup, ideal and congruence growth of free semigroups, arXiv preprint arXiv:1409.2444, 2014
  82. D. H. Bailey, Book Reviews, Math. Comp. 65 (1996), 877-895.
  83. D. H. Bailey, Compendium to BBP formulas
  84. D. H. Bailey and J. M. Borwein, Experimental mathematics: recent developments and future outlook, pp. 51-66 of B. Engquist and W. Schmid, editors, Mathematics Unlimited - 2001 and Beyond, 2 vols., Springer-Verlag, 2001 [ps or pdf].
  85. D. H. Bailey and J. M. Borwein, Experimental mathematics: examples, methods and implications, Notices Amer. Math. Soc. 52 (2005), 502-514.
  86. David H. Bailey and Jonathan M. Borwein, Exploratory Experimentation and Computation, Notices of the AMS, 58 (No. 10, 2011), 1410-1419;
  87. D. H. Bailey, J. M. Borwein, Experimental computation as an ontological game changer: The impact of modern mathematical computation tools on the ontology of mathematics, 2014;
  88. David H. Bailey, Jonathan M. Borwein, David Broadhurst and M. L. Glasser, Elliptic integral evaluations of Bessel moments, arXiv:0801.0891. doi:10.1088/1751-8113/41/20/205203, J. Phys. A 41 (20) (2008) 205203. "This paper contains several proofs of identities that we first conjectured on the basis of numerical investigation, hugely facilitated by access to Sloane's wonderful sequence finder."
  89. David H. Bailey, Jonathan M. Borwein, Olga Caprotti, Ursula Martin, Bruno Salvy, Michela Taufer, Opportunities and Challenges in 21st Century Mathematical Computation: ICERM Workshop Report, 2014;
  90. D. H. Bailey, J. M. Borwein, J. S. Kimberley, Discovery of large Poisson polynomials using the MPFUN-MPFR arbitrary precision software, Preprint 2015;
  91. R. A. Bailey and P. J. Cameron, Latin squares: Equivalents and equivalence, Draft, May 2003.
  92. R. Baillie, Fun With Very Large Numbers, arXiv:1105.3943, 2011
  93. Robert Baillie, Wright's Fourth Prime, arXiv:1705.09741 [math.NT], 2017.
  94. R. Baillie, D. Borwein and J. M. Borwein, Surprising sync sums and integrals, Amer. Math. Monthly, 115 (2008), 888-901.
  95. Reginald Bain, A Musical Scale Generated from the Ratio of Consecutive Primes, Proceedings of Bridges 2015: Mathematics, Music, Art, Architecture, Culture,
  96. W. D. Baird, Cops and robbers on graphs and hypergraphs, MS Thesis, Applied Mathematics, Ryerson University, 2011.
  97. W. D. Baird, A. Beveridge, A. Bonato, P. Codenotti, A. Maurer et al., On the minimum order of k-cop-win graphs, Ryerson Applied Mathematics Laboratory. Technical Report, Ryerson University, 2014; PDF.
  98. Beata Bajorska-Harapińska, Barbara Smoleń, Roman Wituła, On Quaternion Equivalents for Quasi-Fibonacci Numbers, Shortly Quaternaccis, Advances in Applied Clifford Algebras (2019) Vol. 29, 54. doi:10.1007/s00006-019-0969-9 (A006495, A009116, A025712, A087455, A088137, A088138, A099456, A106392, A121621, A121622, A138229, A138230, A139011, A146559, A176333, A190965, A190967, A190968, A213421, A266046)
  99. GN Bakare, SO Makanjuola, Some Results on Properties of Alternating Semigroups, Nigerian Journal of Mathematics and Applications Volume 24,(2015), 184−192;
  100. Alan Richard Baker, Non-Optional Projects: Mathematical and Ethical, Explanation In Ethics And Mathematics: Debunking And Dispensability (2016), 220-235. doi:10.1093/acprof:oso/9780198778592.003.0012 (A069853)
  101. Jonathan Baker, Kevin N. Vander Meulen, Adam Van Tuyl, Shedding vertices of vertex decomposable graphs, arXiv preprint arXiv:1606.04447, 2016; also in Discrete Mathematics (2018) Vol. 341, Issue 12, 3355-3369. doi:10.1016/j.disc.2018.07.029 (A001349, A286284, A286285)
  102. Zack Baker, Properties and Calculations of Constructive Orderings on Z/nZ, Minnesota Journal of Undergraduate Mathematics, [S.l.], v. 4, n. 1, mar. 2019.
  103. M. J. Bakhova, A NUMERICAL INVESTIGATION OF APÉRY-LIKE RECURSIONS AND RELATED PICARD-FUCHS EQUATIONS, Ph. D. Thesis, Math. Dept., Louisiana State University and Agricultural and Mechanical College, 2012; PDF.
  104. Valentin Bakoev, Algorithmic approach to counting certain types of m-ary partitions, Discrete Mathematics, Vol 275 (2004), pp. 17-41.
  105. Valentin P. Bakoev, The recurrence relations in teaching students of informatics, Inf. in Educ. 9 (2010) 159-170.
  106. Valentin Bakoev, Ordinances of the vectors of the n-dimensional Boolean cube in accordance with their weights. PDF (A294648)
  107. Valentin Bakoev, Combinatorial and Algorithmic Properties of One Matrix Structure at Monotone Boolean Functions, arXiv:1902.06110 [cs.DM], 2019. (A000372)
  108. Valentin Bakoev, Fast Computing the Algebraic Degree of Boolean Functions, arXiv:1905.08649 [cs.DM], 2019. (A051459, A294648, A305860, A319511)
  109. Hartosh Singh Bal, Gaurav Bhatnagar, Prime Number Conjectures From the Shapiro Class Structure, arXiv:1903.09619 [math.NT], 2019. See also Integers (2020) Vol. 20, Article A11. PDF (A003306)
  110. Srivatsan Balakrishnan, Suresh Govindarajan and Naveen S. Prabhakar, On the asymptotics of higher-dimensional partitions, arXiv:1105.6231.
  111. B. Balamohan, A. Kuznetsov and Stephen Tanny, "On the Behavior of a Variant of Hofstadter's Q-Sequence", J. Integer Sequences, Volume 10, 2007, Article 07.7.1.
  112. B. Balamohan, Zhiqiang Li, Stephen Tanny, A Combinatorial Interpretation for Certain Relatives of the Conolly Sequence (2008); arXiv:0801.1097 and JIS 11 (2008) 08.2.1
  113. Balasuriya, Sanka; Shparlinski, Igor E.; Winterhof, Arne. An average bound for character sums with some counter-dependent recurrence sequences. Rocky Mt. J. Math. 39, No. 5, 1403-1409 (2009). doi:10.1216/RMJ-2009-39-5-1403
  114. Peter Balazs, Generation and Empirical Investigation of hv-Convex Discrete Sets, in Image Analysis, Lecture Notes in Computer Science, Volume 4522/2007, Springer-Verlag.
  115. Peter Balazs, A benchmark set for the reconstruction of hv-convex discrete sets, Discrete Applied Mathematics 157 (16) 2009 3447-3456
  116. Lucilla Baldini, J Eschgfäller, Random functions from coupled dynamical systems, arXiv preprint arXiv:1609.01750, 2016.
  117. Scott Balchin, David Barnes, Constanze Roitzheim, N-operads and associahedra, arXiv:1905.03797 [math.AT], 2019.
  118. Scott Balchin and Dan Rust, Computations for Symbolic Substitutions, Journal of Integer Sequences, Vol. 20 (2017), Article 17.4.1.
  119. Cory B. H. Ball, The Apprentices' Tower of Hanoi, Electronic Theses and Dissertations, East Tennessee State University. Paper 2512, 2015. (A000325)
  120. Tyler Ball, Joanne Beckford, Paul Dalenberg, Tom Edgar, Tina Rajabi, Title, J. Int. Seq., Vol. 23 (2020), Article 20.3.3. HTML (A034968, A055770, A227154, A230403, A331128)
  121. Tyler Ball, Tom Edgar, and Daniel Juda, Dominance Orders, Generalized Binomial Coefficients, and Kummer’s Theorem, Mathematics Magazine, Vol. 87, No. 2, April 2014, 135-143; doi:10.4169/math.mag.87.2.135.
  122. Taylor Ball, David Galvin, Katie Hyry, Kyle Weingartner, Independent set and matching permutations, arXiv:1901.06579 [math.CO], 2019. (A001405)
  123. Tyler Ball, Rachel Chaiser, Dean Dustin, Tom Edgar, Paul Lagarde, Some combinatorics from Zeckendorf representations, Involve (2019) Vol. 12, No. 7, 1241–1260. doi:10.2140/involve.2019.12.1241
  124. Cristina Ballantine, Richard Bielak, Combinatorial proofs of two Euler type identities due to Andrews, arXiv:1803.06394 [math.CO], 2018. (A090867, A265251)
  125. Cristina Ballantine, Mircea Merca, Bisected theta series, least r-gaps in partitions, and polygonal numbers, arXiv:1710.05960 [math.CO], 2017. (A022567, A064174, A064428)
  126. C Ballantine, M Merca, Padovan numbers as sums over partitions into odd parts, Journal of Inequalities and Applications, (2016) 2016:1. doi:10.1186/s13660-015-0952-5
  127. Cristina Ballantine, Mircea Merca, New convolutions for the number of divisors Journal of Number Theory, 2016, vol. 170, pp. 17-34; doi:10.1016/j.jnt.2016.06.007
  128. Cristina Ballantine, M Merca, Parity of sums of partition numbers and squares in arithmetic progressions, The Ramanujan Journal, 2016 doi:10.1007/s11139-016-9845-6
  129. Cristina Ballantine, Mircea Merca, Jacobi’s Four and Eight Squares Theorems and Partitions into Distinct Parts, Mediterranean Journal of Mathematics (2019) Vol. 16, No. 2, 26. doi:10.1007/s00009-019-1301-6 (A101277)
  130. Cristina Ballantine, Mircea Merca, Combinatorial Proof of the Minimal Excludant Theorem, arXiv:1908.06789 [math.NT], 2019.
  131. Cristina Ballantine, Mircea Merca, On identities of Watson type, Ars Mathematica Contemporanea (2019) Vol. 17, 277–290. doi:10.26493/1855-3974.1782.127 (A015744, A038348)
  132. Cristina Ballantine, Amanda Welch, Beck-type identities for Euler pairs of order $r$, arXiv:2006.02335 [math.NT], 2020. (A090867, A265251)
  133. Christian Ballot, On Functions Expressible as Words on a Pair of Beatty Sequences, Journal of Integer Sequences, Vol. 20 (2017), Article 17.4.2.
  134. Christian Ballot, Divisibility of the middle Lucasnomial coefficient, Fib. Q., 55 (2017, 297-308.
  135. Balof, Barry, Restricted tilings and bijections. J. Integer Seq. 15 (2012), no. 2, Article 12.2.3, 17 pp.
  136. Barry Balof and Jacob Menashe, "Semiorders and Riordan Numbers", J. Integer Sequences, Volume 10, 2007, Article 07.7.6.
  137. B. Balof, H. Jenne, Tilings, Continued Fractions, Derangements, Scramblings, and e, - Journal of Integer Sequences, 17 (2014), #14.2.7.
  138. Ferenc Balogh, A generalization of Gessel's generating function to enumerate words with double or triple occurrences in each letter and without increasing subsequences of a given length, preprint arXiv:1505.01389, 2015.
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  274. Tal Barnea, The Riemann Zeta Function and the Fractional Part of Rational Powers, J. Int. Seq., Vol. 22 (2019), Article 19.3.6. HTML (A013697)
  275. Joel Barnes, Conformal welding of uniform random trees, Ph. D. Dissertation, Univ. Washington, 2014;
  276. M. P. Barnett, Some applications of high precision arithmetic
  277. Brandy Amanda Barnette, Counting Convex Sets on Products of Totally Ordered Sets, Masters Theses & Specialist Projects, Paper 1484, 2015 (A002415, A000332, A006542, A006857, A108679)
  278. D Barrera, MJ Ibáñez, S Remogna, On the construction of trivariate near-best quasi-interpolants based on C^2 quartic splines on type-6 tetrahedral partitions, Journal of Computational and Applied, 2016, Volume 311, February 2017, Pages 252-261.
  279. Christian Barrientos, Sarah Minion, Enumerating Families of Labeled Graphs, Journal of Integer Sequences, 18 (2015), # 15.1.7.
  280. Christian Barrientos, Sarah Minion, On the Graceful Cartesian Product of Alpha-Trees, Theory and Applications of Graphs, Vol. 4: Iss. 1, Article 3, 2017. doi:10.20429/tag.2017.040103
  281. Christian Barrientos, Sarah Minion, On the number of α-labeled graphs, Discussiones Mathematicae Graph Theory, to appear, doi:10.7151/dmgt.1985
  282. Christian Barrientos, Sarah Minion, Series-Parallel Operations with Alpha-Graphs, Theory and Applications of Graphs (2019) Vol. 6, Issue 1, Article 4. Abstract (A032121)
  283. Michael D. Barrus, Weakly threshold graphs, arXiv preprint arXiv:1608.01358, 2016
  284. M. D. Barrus, S. G. Hartke, Minimal forbidden sets for degree sequence characterizations, 2013; PDF
  285. Paul Barry, "A Catalan Transform and Related Transformations on Integer Sequences", J. Integer Sequences, Volume 8, 2005, Article 05.4.5.
  286. Paul Barry, "On Integer-Sequence-Based Constructions of Generalized Pascal Triangles", J. Integer Sequences, Volume 9, 2006, Article 06.2.4.
  287. Paul Barry, "On a Family of Generalized Pascal Triangles Defined by Exponential Riordan Arrays", J. Integer Sequences, Volume 10, 2007, Article 07.3.5.
  288. Paul Barry, "Some Observations on the Lah and Laguerre Transforms of Integer Sequences", J. Integer Sequences, Volume 10, 2007, Article 07.4.6.
  289. Paul Barry, On Integer Sequences Associated With the Cyclic and Complete Graphs, J. Integer Sequences, Volume 10, 2007, Article 07.4.8.
  290. Paul Barry, A Note on Krawtchouk Polynomials and Riordan Arrays, JIS 11 (2008) 08.2.2
  291. Paul Barry, A Study of Integer Sequences, Riordan Arrays, Pascal-like Arrays and Hankel Transforms, Ph D Thesis, University College, Cork, Republic of Ireland (2009).
  292. P. Barry, A Note on a One-Parameter Family of Catalan-Like Numbers, JIS 12 (2009) 09.5.4
  293. P. Barry, Continued fractions and transformations of integer sequences, JIS 12 (2009) 09.7.6
  294. P. Barry, Symmetric Third-Order Recurring Sequences, Chebyshev Polynomials, and Riordan Arrays, JIS 12 (2009) 09.8.6
  295. P. Barry, Generalized Catalan Numbers, Hankel Transforms and Somos-4 Sequences, J. Int. Seq. 13 (2010) #10.7.2.
  296. P. Barry, The Restricted Toda Chain, Exponential Riordan Arrays, and Hankel Transforms, J. Int. Seq. 13 (2010) # 10.8.4
  297. P. Barry, Exponential Riordan Arrays and Permutation Enumeration, J. Int. Seq. 13 (2010) # 10.9.1
  298. Barry, Paul, Riordan arrays, orthogonal polynomials as moments, and Hankel transforms. J. Integer Seq. 14 (2011), no. 2, Article 11.2.2, 37 pp.
  299. Barry, Paul, On the central coefficients of Bell matrices. J. Integer Seq. 14 (2011), no. 4, Article 11.4.3, 10 pp.
  300. Barry, Paul, On a generalization of the Narayana triangle. J. Integer Seq. 14 (2011), no. 4, Article 11.4.5, 22 pp.
  301. Paul Barry, Eulerian polynomials as moments, via exponential Riordan arrays, Arxiv preprint arXiv:1105.3043, 2011, and JIS 14 (2011) # 11.9.5
  302. Paul Barry, Combinatorial polynomials as moments, Hankel transforms and exponential Riordan arrays, Arxiv preprint arXiv:1105.3044, 2011, also J. Int. Seq. 14 (2011) 11.6.7.
  303. P. Barry, Invariant number triangles, eigentriangles and Somos-4 sequences, Arxiv preprint arXiv:1107.5490, 2011.
  304. P. Barry, On sequences with {-1, 0, 1} Hankel transforms, Arxiv preprint arXiv:1205.2565, 2012
  305. P. Barry, A Note on Three Families of Orthogonal Polynomials defined by Circular Functions, and Their Moment Sequences, Journal of Integer Sequences, Vol. 15 (2012), #12.7.2.
  306. P. Barry, Riordan-Bernstein Polynomials, Hankel Transforms and Somos Sequences, Journal of Integer Sequences, Vol. 15 2012, #12.8.2.
  307. Paul Barry, On the Hurwitz Transform of Sequences, Journal of Integer Sequences, Vol. 15 (2012), #12.8.7.
  308. P. Barry, On the Hankel transform of C-fractions, arXiv preprint arXiv:1212.3490, 2012
  309. P. Barry, On the Central Coefficients of Riordan Matrices, Journal of Integer Sequences, 16 (2013), #13.5.1.
  310. P. Barry, A Note on a Family of Generalized Pascal Matrices Defined by Riordan Arrays, Journal of Integer Sequences, 16 (2013), #13.5.4.
  311. P. Barry, On the Inverses of a Family of Pascal-Like Matrices Defined by Riordan Arrays, Journal of Integer Sequences, 16 (2013), #13.5.6.
  312. P. Barry, On the Connection Coefficients of the Chebyshev-Boubaker polynomials, The Scientific World Journal, Volume 2013 (2013), Article ID 657806, 10 pages; doi:10.1155/2013/657806.
  313. Paul Barry, Laurent Biorthogonal Polynomials and Riordan Arrays, arXiv preprint arXiv:1311.2292, 2013
  314. P. Barry, General Eulerian Polynomials as Moments Using Exponential Riordan Arrays, Journal of Integer Sequences, 16 (2013), #13.9.6.
  315. P. Barry, Embedding structures associated with Riordan arrays and moment matrices, arXiv preprint arXiv:1312.0583, 2013
  316. P. Barry, Comparing two matrices of generalized moments defined by continued fraction expansions, arXiv preprint arXiv:1311.7161, 2013 and J. Int. Seq. 17 (2014) # 14.5.1
  317. P. Barry, Generalized Stirling Numbers, Exponential Riordan Arrays, and Toda Chain Equations, Journal of Integer Sequences, 17 (2014), #14.2.3.
  318. P. Barry, Constructing Exponential Riordan Arrays from Their A and Z Sequences, Journal of Integer Sequences, 17 (2014), #14.2.6.
  319. P Barry, Riordan arrays, generalized Narayana triangles, and series reversion, Linear Algebra and its Applications, 491 (2016) 343–385.
  320. Paul Barry, Riordan Arrays: A Primer, Logic Press, 2016.
  321. Paul Barry, Jacobsthal Decompositions of Pascal's Triangle, Ternary Trees, and Alternating Sign Matrices, - Journal of Integer Sequences, 19, 2016, #16.3.5.
  322. Paul Barry, On the Group of Almost-Riordan Arrays, arXiv preprint arXiv:1606.05077, 2016
  323. Paul Barry, Eulerian-Dowling Polynomials as Moments, Using Riordan Arrays, arXiv:1702.04007 [math.CO], 2017.
  324. Paul Barry, A Note on d-Hankel Transforms, Continued Fractions, and Riordan Arrays, arXiv:1702.04011 [math.CO], 2017.
  325. Paul Barry, Sigmoid functions and exponential Riordan arrays, arXiv:1702.04778 [math.CA], 2017.
  326. Paul Barry, Power series, the Riordan group and Hopf algebras, arXiv:1706.01323 [math.CO], 2017.
  327. Paul Barry, On a transformation of Riordan moment sequences, arXiv:1802.03443 [math.CO], 2018. (A000108, A000142, A000629, A000670, A001003, A001006, A001586, A005043, A006318, A008292, A064641, A021009, A049774, A049774, A052186, A052709, A060187, A090181, A097899, A097899, A111961, A123125, A129775, A131198, A173018)
  328. Paul Barry, Three Études on a sequence transformation pipeline, arXiv:1803.06408 [math.CO], 2018. (A000045, A000108, A000670, A000957, A001263, A001519, A002105, A003688, A004123, A008292, A019538, A028246, A032033, A033282, A038754, A046802, A048993, A052948, A060693, A074059, A075497, A078008, A086810, A090181, A090582, A094416, A094417, A094418, A094503, A096078, A100754, A123125, A126216, A130850, A131198, A133494, A151575, A173018, A176230, A211402, A211608, A248727, A271697) "This note makes reference to many sequences to be found in the OEIS, which at the time of writing contains more than 300,000 sequences. All who work in the area of integer sequences are profoundly indebted to Neil Sloane. Many of the sequences in this note are related to simplicial objects such as the associahedron and the permutahedron. Indeed, the T-transform provides an enumerative link between these two objects, while the P pipeline brings these two objects back to more basic objects. The comments of Tom Copeland and Peter Bala in the relevant OEIS entries have been very useful in this context."
  329. Paul Barry, Generalized Eulerian Triangles and Some Special Production Matrices, arXiv:1803.10297 [math.CO], 2018. (A000108, A000165, A000670, A008292, A060187, A108524, A114608, A118376, A123125, A151374, A173018)
  330. Paul Barry, The Gamma-Vectors of Pascal-like Triangles Defined by Riordan Arrays, arXiv:1804.05027 [math.CO], 2018. (A000108, A000898, A001263, A001591, A007318, A008288, A008292, A055151, A059344, A077938, A100861, A100862, A101280, A271875)
  331. Paul Barry, A note on number triangles that are almost their own production matrix, arXiv:1804.06801 [math.CO], 2018. (A001339, A003319, A081923, A094587, A104980, A111184, A111529, A111530, A111531, A111536, A111544, A111553, A132159)
  332. Paul Barry, On the f-Matrices of Pascal-like Triangles Defined by Riordan Arrays. arXiv:1805.02274 [math.CO], 2018. (A001147, A001263, A007318, A019538, A033282, A038207, A055151, A074909, A101280, A135278)
  333. Paul Barry, Riordan Pseudo-Involutions, Continued Fractions and Somos 4 Sequences, arXiv:1807.05794 [math.CO], 2018. (A000108, A000245, A004148, A006196, A006769, A007477, A023431, A025227, A025243, A025250, A025258, A025273, A050512, A060693, A068875, A086246, A089796, A090181, A091561, A091565, A105633, A130749, A152225, A178075, A178622, A178627, A187256, A217333)
  334. Paul Barry, The Central Coefficients of a Family of Pascal-like Triangles and Colored Lattice Paths, J. Int. Seq., Vol. 22 (2019), Article 19.1.3. HTML (A000108, A000984, A001405, A001700, A007318, A008288, A026003, A054341, A060693, A060899, A081577, A107230, A110109)
  335. Paul Barry, On the halves of a Riordan array and their antecedents, arXiv:1906.06373 [math.CO], 2019. (A007318, A264772)
  336. Paul Barry, On the r-shifted central triangles of a Riordan array, arXiv:1906.01328 [math.CO], 2019. (A007318)
  337. Paul Barry, Generalized Catalan Numbers Associated with a Family of Pascal-like Triangles, J. Int. Seq., Vol. 22 (2019), Article 19.5.8. HTML (A000108, A000984, A001006, A006318, A007318, A008288, A009766, A033184, A033282, A039598, A047891, A054726, A060693, A064063, A064641, A078740, A080247, A082298, A082301, A082302, A086810, A088617, A090442, A090452, A103210, A103211, A108524, A126216, A131198, A133305, A152600, A152601, A156017, A269730, A269731, A281260)
  338. Paul Barry, A Note on Riordan Arrays with Catalan Halves, arXiv:1912.01124 [math.CO], 2019. (A000108, A001316, A001519, A001700, A001906, A007318, A033184, A039598, A063886, A078008, A094527, A106566, A112466, A112467, A125187, A125187, A128899, A258431)
  339. Paul Barry, Chebyshev moments and Riordan involutions, arXiv:1912.11845 [math.CO], 2019. (A000045, A000108, A001764, A005156, A007318, A033184, A035929, A039598, A051255, A081696, A098746, A106566, A107842, A109262, A109267, A128899, A182486, A225887)
  340. Paul Barry, Riordan arrays, the A-matrix, and Somos 4 sequences, arXiv:1912.01126 [math.CO], 2019. (A000045, A000108, A001045, A005043, A006318, A006720, A006769, A007863, A097609, A104545, A151374, A162547, A171416, A178628, A215661)
  341. Paul Barry, Characterizations of the Borel triangle and Borel polynomials, arXiv:2001.08799 [math.CO], 2020. (A000007, A000012, A000045, A000108, A001006, A001045, A001764, A002293, A002294, A006013, A006632, A007318, A009766, A025235, A033999, A036765, A036766, A052709, A062992, A064641, A071356, A071948, A085880, A092276, A118971, A122871, A234950)
  342. Paul Barry, On a Central Transform of Integer Sequences, arXiv:2004.04577 [math.CO], 2020. (A000032, A000034, A000245, A000346, A000957, A001263, A002249, A004442, A007318, A007854, A010872, A026012, A028242, A029635, A029651, A039599, A055248, A072547, A077021, A078008, A094527, A097070, A099324, A100320, A106566, A106853, A107920, A110162, A115140, A118973, A118973, A129869, A141223, A151821, A158499, A158500, A187307, A266724, A272931)
  343. Paul Barry, On the Central Antecedents of Integer (and Other) Sequences, J. Int. Seq., Vol. 23 (2020), Article 20.8.3. Abstract (A000027, A000041, A000108, A000203, A000984, A002426, A005043, A007317, A025174, A214776)
  344. Paul Barry and Patrick Fitzpatrick, "On a One-Parameter Family of Riordan Arrays and the Weight Distribution of MDS Codes", J. Integer Sequences, Volume 10, 2007, Article 07.9.8.
  345. P. Barry, A. Hennessey, Notes on a Family of Riordan Arrays and Associated Integer Hankel Transforms, JIS 12 (2009) 09.5.3
  346. P. Barry, A. Hennessy, The Euler-Seidel Matrix, Hankel Matrices and Moment Sequences, J. Int. Seq. 13 (2010) # 10.8.2
  347. P. Barry, A. Hennessy, Meixner-Type Results for Riordan Arrays and Associated Integer Sequences, J. Int. Seq. 13 (2010) # 10.9.4
  348. P. Barry and A. Hennessy, Four-term Recurrences, Orthogonal Polynomials and Riordan Arrays, Journal of Integer Sequences, 2012, article 12.4.2.
  349. Barry, Paul; Hennessy, Aoife A note on Narayana triangles and related polynomials, Riordan arrays, and MIMO capacity calculations. J. Integer Seq. 14 (2011), no. 3, Article 11.3.8, 26 pp.
  350. Barry, Paul; Hennessy, Aoife Four-term recurrences, orthogonal polynomials and Riordan arrays. J. Integer Seq. 15 (2012), no. 4, Article 12.4.2, 19 pp.
  351. Paul Barry and Aoife Hennessy, Generalized Narayana Polynomials, Riordan Arrays, and Lattice Paths, Journal of Integer Sequences, Vol. 15, 2012, #12.4.8.
  352. Paul Barry, Aoife Hennessy, Nikolaos Pantelidis, Algebraic properties of Riordan subgroups, ResearchGate preprint (2020). Abstract (A000012, A000045, A000108, A004148)
  353. Paul Barry, Arnauld Mesinga Mwafise, Classical and Semi-Classical Orthogonal Polynomials Defined by Riordan Arrays, and Their Moment Sequences, Journal of Integer Sequences, Vol. 21 (2018), Article 18.1.5. HTML (A000045, A000108, A000984, A001045, A001147, A049027, A059304, A081696, A098614, A200375)
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