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"This continued fraction ought to be classical, but the first mention of which I am aware is a 2006 contribution to the OEIS by an amateur mathematician, Paul D. Hanna, who found it empirically; it was proven a few years later by Josuat-Vergès [49] by a combinatorial method (which also yields a q-generalization)." [Alan D. Sokal, 2018]

"This work was immeasurably facilitated by the On-Line Encyclopedia of Integer Sequences [16]. I warmly thank Neil Sloane for founding this indispensable resource, and the hundreds of volunteers for helping to maintain and expand it." [Alan D. Sokal, 2019]

"Using the On-Line Encyclopedia of Integer Sequences (OEIS), we have seen that quite different sequences can have the same binary operators. We have also found integer sequences not given in OEIS and that need to be studied." [Amelia Carolina Sparavigna, 2019]

"There is a Web Page: <> by N.J.A. Sloane. It tells, from typing the first few terms of a sequence, whether that sequence has occurred somewhere else in Mathematics. Postgraduate student Daniel Steffen traced this down and found, to our surprise, that the sequence was related to the tangent function tan x. Ryan and Tam searched out what was known about this connection and discovered some apparently new results. We all found this a lot of fun and I hope you will too." [Ross Street, 2015]

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  1. Paul B. Slater, Eigenvalues, Separability and Absolute Separability of Two-Qubit States (2008); arXiv:0805.0267
  2. Paul B. Slater, Formulas for Generalized Two-Qubit Separability Probabilities, arXiv:1609.08561 2016.
  3. Paul B. Slater, Hypergeometric/Difference-Equation-Based Separability Probability Formulas and Their Asymptotics for Generalized Two-Qubit States Endowed with Random Induced Measure, preprint arXiv:1504.04555, 2015. (A004523, A232007)
  4. Peter J. Slater, It Is All Labeling, In: Gera R., Hedetniemi S., Larson C. (eds) Graph Theory. Problem Books in Mathematics. Springer, 2016, doi:10.1007/978-3-319-31940-7_6
  5. Michael C. Slattery, Groups with at most twelve subgroups, arXiv preprint arXiv:1607.01834, 2016
  6. Richard M. Slevinsky, On the use of Hahn's asymptotic formula and stabilized recurrence for a fast, simple, and stable Chebyshev-Jacobi transform, arXiv preprint arXiv:1602.02618, 2016
  7. Arkadii Slinko, Algebra for Applications: Cryptography, Secret Sharing, Error-Correcting, Fingerprinting, Compression, Springer 2015.
  8. N. J. A. Sloane, A handbook of integer sequences, Academic Press (1973)
  9. N. J. A. Sloane, An on-line version of "The Encylopedia of Integer Sequences", Electron. J. Comb. 1 (1994) 179-183
  10. N. J. A. Sloane, The Sphere Packing Problem, Proceedings Internat. Congress Math. Berlin 1998, Documenta Mathematika, III (1998), pp. 387-396. (pdf)
  11. N. J. A. Sloane, My Favorite Integer Sequences, in Sequences and their Applications (Proceedings of SETA '98), C. Ding, T. Helleseth and H. Niederreiter (editors), Springer-Verlag, London, 1999, pp. 103-130.
  12. N. J. A. Sloane, On Single-Deletion Correcting Codes, in K. T. Arasu and A. Seress, eds., Codes and Designs, Ohio State University, May 2000 (Ray-Chaudhuri Festschrift), Walter de Gruyter, Berlin, 2002, pp. 273-291.
  13. N. J. A. Sloane, The Sphere-Packing Problem (2002), arXiv:math/0207256.
  14. N. J. A. Sloane, The On-Line Encyclopedia of Integer Sequences (2003), arXiv:math/0312448; Notices Amer. Math. Soc., 50 (September 2003), pp. 912-915.
  15. N. J. A. Sloane, arXiv:0912.2394 Seven Staggering Sequences.
  16. N. J. A. Sloane, Gleason's theorem on self-dual codes and its generalizations (talk given at Conference on Algebraic Combinatorics in honor of Eiichi Bannai, Sendai, Japan, June 2006).
  17. N. J. A. Sloane, Eight Hateful Sequences, arXiv:0805.2128 (2008). See also Ch. 1, Barrycades and Septoku: Papers in Honor of Martin Gardner and Tom Rodgers, AMS/MAA Spectrum (2020) Vol. 100, 4-9. (A000203, A001008, A002805, A003001, A006960, A033865, A051003, A064413, A090822, A130316, A130838, A131286, A131287, A131744, A131745, A131746, A133242, A133500, A133816, A133817, A134204, A135385, A135473, A135475, A138563)
  18. N. J. A. Sloane, 2178 And All That, PDF and Fibonacci Q. 52 (2) (2014) 99-120
  19. N. J. A. Sloane, The on-line encyclopedia of integer sequences, Ann. Math. Inform. 41 (2013) 219-234
  20. N. J. A. Sloane, 2178 And All That, Video of talk given in Doron Zeilberger's Experimental Math Seminar at Rutgers University, Oct. 10 2013: <a href="">Part 1</a>, <a href="">Part 2</a>.
  21. N. J. A. Sloane, On the Number of ON Cells in Cellular Automata, arXiv:1503.01168, 2015
  22. N. J. A. Sloane, The On-Line Encyclopedia of Integer Sequences, Notices, Amer. Math. Soc., 65 (No. 9, Oct. 2018), 1062-1074 doi:10.1090/noti1734. Reprinted in "The Best Writing on Mathematics 2019", ed. M. Pitici, Princeton Univ. Press, 2019, pp. 90-119 and colored illustrations following page 80.
  23. N. J. A. Sloane and Parthasarathy Nambi, Integer Sequences Related to Chemistry, pdf, Poster presented at the Amer. Chem. Soc. National Meeting, San Francisco, Fall 2006.
  24. N. J. A. Sloane and J. A. Sellers, arXiv:math.CO/0312418 On non-squashing partitions], Discrete Math., 294 (2005), no. 3, 259-274.
  25. N. J. A. Sloane and Thomas Wieder, arXiv:math.CO/0307064 The Number of Hierarchical Orderings, arXiv:math.CO/0307064, also doi:10.1007/s11083-004-9460-9 Orderings, Order 21 (2004), no. 1, 83-89.
  26. Slomczynska, Katarzyna Free spectra of linear equivalential algebras. J. Symbolic Logic 70 (2005), no. 4, 1341-1358.
  27. Michael Small, C.K. Tse, David M. Walker, Super-spreaders and the rate of transmission of the SARS virus, Physica D: Nonlinear Phenomena, Volume 215, Issue 2, 15 March 2006, Pages 146-158.
  28. F. Smarandache, arXiv:math.GM/0010137 Another Set of Sequences, Sub-Sequences and Sequences of Sequences, Partially published in "Only Problems, Not Solutions!", by Florentin Smarandache, Xiquan Publ. Hse., Phoenix, 1991.
  29. F. Smarandache, arXiv:math.GM/0010132 Considerations on New Functions in Number Theory, Partially inlcuded in the book "Noi Functii in Teoria Numerelor", by Florentin Smarandache, University of Kishinev Press, 120 p., 1999.
  30. F. Smarandache, arXiv:math.GM/0010125 A Set of Sequences in Number Theory], Presented to the Pedagogical High School Student Conference in Craiova, 1972. "Collected Papers", Vol. II, book by Florentin Smarandache, University of Kishinev Press, Kishinev, 200 p., 1997.
  31. F. Smarandache, arXiv:math.GM/0010151 G Add-On, Digital, Sieve, General Periodical and Non-Arithmetic Sequences.
  32. Florentin Smarandache, Numerology (2000), arXiv:math.GM/0010132.
  33. Florentin Smarandache, Sequences of Numbers Involved in Unsolved Problems (2006), arXiv:math.GM/0604019.
  34. F. Smarandache, Generalization and alternatives of Kaprekar's routine, arXiv:1005.3235
  35. Florentin Smarandache, Jean Dezert, An Introduction to the DSm Theory for the Combination of Paradoxical, Uncertain and Imprecise Sources of Information (2006), arXiv:cs/0608002.
  36. Florentin Smarandache, Jean Dezert, The Combination of Paradoxical, Uncertain and Imprecise Sources of Information based on DSmT and Neutro-Fuzzy Inference, arXiv:cs/0412091 (2004)
  37. Yotam Smilansky, Yaar Solomon, Multiscale Substitution Tilings, arXiv:2003.11735 [math.DS], 2020. (A328074)
  38. David M. Smith, Geoffrey Smith, Tight Bounds on Information Leakage from Repeated Independent Runs, 2017 IEEE 30th Computer Security Foundations Symposium (CSF). doi:10.1109/CSF.2017.18
  39. Hanson Smith, Ramification in the Division Fields of Elliptic Curves and an Application to Sporadic Points on Modular Curves, arXiv:1808.04809 [hep-th], 2018. (A085548)
  40. Jason P. Smith, A Formula for the Mobius function of the Permutation Poset Based on a Topological Decomposition, arXiv preprint arXiv:1506.04406, 2015
  41. K. W. Smith, KWSnet Mathematics Index, 2015;
  42. Barry R. Smith, Reducing quadratic forms by kneading sequences, J. Int. Seq. 17 (2014) 14.11.8.
  43. Hanson Smith, Ramification in Division Fields and Sporadic Points on Modular Curves, U. Conn. (2020). PDF (A085548)
  44. Jason P. Smith, The poset of graphs ordered by induced containment, arXiv:1806.01821 [math.CO], 2018. (A088617)
  45. R. Smith and V. Vatter, A stack and a pop stack in series, arXiv preprint arXiv:1303.1395, 2013
  46. V. N. Smith and L. Shapiro, Catalan numbers, Pascal's triangle and mutators, Congressus Numerant., 205 (2010), 187-197.
  47. Barbara Smoleń, Roman Wituła, Two-parametric quasi-Fibonacci numbers, Silesian J. Pure Appl. Math. (2017), Vol. 7, Is. 1, pp. 99-121. PDF (A000045, A001519, A001906, A014445, A015448, A020699, A028495, A030191, A052975, A074872, A081567, A081568, A081569, A081571, A081574, A094831, A096976, A099453, A120757, A122100, A123941, A124292, A147704, A163073, A163306, A181879, A188168)
  48. C. Smyth, The terms in Lucas sequences divisible by their indices, J. Int. Seq. 13 (2010) 10.2.4
  49. Snellman, Jan, Standard paths in another composition poset. Electron. J. Combin. 11 (2004), no. 1, Research Paper 76, 8 pp.
  50. Jan Snellman, Digraphs with a fixed number of edges and vertices, having a maximal number of walks of length 2 (2008); arXiv:0804.4655
  51. Jan Snellman and Michael Paulsen, "Enumeration of Concave Integer Partitions", J. Integer Sequences, Volume 7, 2004, Article 04.1.3.
  52. Marie A. Snipes, LA Ward, Harmonic measure distributions of planar domains: a survey, The Journal of Analysis, December 2016, Volume 24, Issue 2, pp 293–330.
  53. Aaron Snook, Augmented Integer Linear Recurrences,, 2012.
  54. D. R. Snow, Problems and Remarks, 18th International Symposium on Functional Equations, 1980, Remark 18. (ps, pdf)
  55. E. V. K. Sobolev, A survey of the cell-growth problem and some its variations, preprint, Mar. 2001.
  56. Joram Soch, Expressing the Indefinite Integral of the Standard Normal Probability Density Function, arXiv preprint arXiv:1512.04858, 2015
  57. Joram Soch, Linear Algebraic Number Theory, Part I: Foundations, arXiv:1709.05959 [math.GM], 2017.
  58. Edwin Soedarmadji, Latin hypercubes and MDS codes, Discrete Mathematics, Volume 306, Issue 12, 28 June 2006, Pages 1232-1239.
  59. Anthony Sofo, Fibonacci and Some of His Relations
  60. Takehide Soh, Packing Consequtive Squares into a Sqaure (sic), Kobe University (Japan, 2019). PDF (A005842)
  61. A. D. Sokal, The leading root of the partial theta function, arXiv:1106.1003, 2011, and Adv. Math. 229, No. 5, 2603-2621 (2012).
  62. Alan D. Sokal, The Euler and Springer numbers as moment sequences, arXiv:1804.04498 [math.CO], 2018. (A000111, A000464, A001586, A085734, A088874, A098906) "This continued fraction ought to be classical, but the first mention of which I am aware is a 2006 contribution to the OEIS by an amateur mathematician, Paul D. Hanna, who found it empirically; it was proven a few years later by Josuat-Vergès [49] by a combinatorial method (which also yields a q-generalization)."
  63. Alan D. Sokal, Vertically constrained Motzkin-like paths inspired by bobbin lace, arXiv:1804.08919 [math.CO], 2018. (A260492)
  64. Alan D. Sokal, A remark on the enumeration of rooted labeled trees, arXiv:1910.14519 [math.CO], Oct. 2019. Also Discrete Math., 341 (2020), #111865. (Sequences A071207, A232006.) [This work was immeasurably facilitated by the On-Line Encyclopedia of Integer Sequences. I warmly thank Neil Sloane for founding this indispensable resource, and the hundreds of volunteers for helping to maintain and expand it.]
  65. Alpha Soko, James Makungu, Soliton Distribution in the Ball and Box Cellular Automation Model, American Journal of Mathematical and Computer Modelling (2019) Vol. 4, Issue 1, 27-30. doi:10.11648/j.ajmcm.20190401.14
  66. Patrick Sole and Michel Planat, THE ROBIN INEQUALITY FOR 7-FREE INTEGERS, INTEGERS, 2011, #A65;
  67. Fernando Soler-Toscano and Hector Zenil, A Computable Measure of Algorithmic Probability by Finite Approximations with an Application to Integer Sequences, arXiv:1504.06240 [cs.IT], 2017.
  68. Allan I. Solomon, Gerard Duchamp, Pawel Blasiak et al., Normal Order: Combinatorial Graphs (2004), arXiv:quant-ph/0402082.
  69. A. I. Solomon, C.-L. Ho and G. H. E. Duchamp, Degrees of entanglement for multipartite systems, Arxiv preprint arXiv:1205.4958, 2012
  70. N. Solomon, S. Solomon, A natural extesion of Catalan numbers, JIS 11 (2008) 08.3.5.
  71. Liam Solus, Simplices for Numeral Systems, arXiv:1706.00480 [math.CO], 2017.
  72. Liam Solus, Local h*-Polynomials of Some Weighted Projective Spaces, arXiv:1807.08223 [math.CO], 2018. (A002301)
  73. Steven E. Sommars and Tim Sommars, "The Number of Triangles Formed by Intersecting Diagonals of a Regular Polygon", J. Integer Sequences, Volume 1, 1998, Article 98.1.5.
  74. Michael Somos, A Multisection of q-Series, (A007325, A108483, A058531)
  75. Michael Somos, A Remarkable eta-product Identity, (A143751, A058728)
  76. Jonathan Sondow, New Vacca-Type Rational Series for Euler's Constant and Its "Alternating" Analog ln(4/Pi) (2005), arXiv:math.NT/0508042.
  77. Sondow, Jonathan, A geometric proof that e is irrational and a new measure of its irrationality. Amer. Math. Monthly 113 (2006), no. 7, 637-641.
  78. Jonathan Sondow, Which Partial Sums of the Taylor Series for e are Convergents to e? (and a Link to the Primes 2, 5, 13, 37, 463, ...) with an Appendix by Kyle Schalm (2007), arXiv:0709.0671.
  79. Jonathan Sondow, Ramanujan primes and Bertrand's postulate, Amer. Math. Monthly, 116 (2009), 630-635.
  80. Sondow, Jonathan; and Hadjicostas, Petros, The generalized-Euler-constant function gamma(z) and a generalization of Somos's quadratic recurrence constant. J. Math. Anal. Appl. 332 (2007), no. 1, 292-314.
  81. J. Sondow and K. MacMillan, Primary pseudoperfect numbers, arithmetic progressions, and the Erdős-Moser equation, Amer. Math. Monthly, 124 (2017)232-240. doi:10.4169/amer.math.monthly.124.3.232
  82. J. Sondow, J. W. Nicholson and T. D. Noe, Ramanujan Primes: Bounds, Runs, Twins, and Gaps, Arxiv preprint arXiv:1105.2249, 2011. J. Integer Seq. 14 (2011) Article 11.6.2.
  83. J. Sondow, E. Tsukerman, The p-adic Order of Power Sums, the Erdos-Moser Equation, and Bernoulli Numbers, arXiv preprint arXiv:1401.0322, 2014.
  84. Nikki Sonenberg, Peter G. Taylor, Networks of interacting stochastic fluid models with infinite and finite buffers, Queueing Systems (2019) Vol. 92, Issue 3–4, 293–322. doi:10.1007/s11134-019-09619-w
  85. Chunwei Song, Bowen Yao, On Combinatorial Rectangles with Minimum ∞-Discrepancy, arXiv:1909.05648 [math.CO], 2019. (A002896)
  86. H.-Y. Song and J. B. Lee, On (n,k)-sequences, Discrete Appl. Math. 105, No.1-3, 183-192 (2000).
  87. Eric Sopena, i-Mark: A new subtraction division game, arXiv:1509.04199, 2015
  88. Henrik Kragh Sørensen, “The End of Proof”? The Integration of Different Mathematical Cultures as Experimental Mathematics Comes of Age, in Mathematical Cultures, pp 139-160 (2016); doi:10.1007/978-3-319-28582-5_9
  89. J. Sorenson, J. Webster, Strong pseudoprimes to twelve prime bases, arXiv:1509.00864. See first page.
  90. Jonathan P. Sorenson, Jonathan Webster, Two Algorithms to Find Primes in Pattern, arXiv:1807.08777 [math.NT], 2018. (A005602, A007508, A050258)
  91. Øystein Sørensen, Marta Crispino, Qinghua Liu, Valeria Vitelli, BayesMallows: An R Package for the Bayesian Mallows Model, arXiv:1902.08432 [stat.CO], 2019.
  92. Brianna Sorenson, Jonathan P Sorenson, Jonathan Webster, An Algorithm and Estimates for the Erdős-Selfridge Function (work in progress), arXiv:1907.08559 [math.NT], 2019. (A003458)
  93. José Ezequiel Soto Sánchez, Asla Medeiros e Sá, Luiz Henrique de Figueiredo, Acquiring periodic tilings of regular polygons from images, The Visual Computer (2019) Vol. 35, Issue 6–8, 899–907. doi:10.1007/s00371-019-01665-y (A299780)
  94. Jakub Souček, Ondrej Janíčko, Reverse Fibonacci sequence and its description, (2019). PDF (A057084)
  95. Soulé, Christophe (13 Feb 2008). “Le triangle de Pascal et ses propriétés”. 
  96. Richard Southwell and Jianwei Huang, Complex Networks from Simple Rewrite Systems, Arxiv preprint arXiv:1205.0596, 2012.
  97. Jeremiah T. Southwick, Two Inquiries Related to the Digits of Prime Numbers, Ph. D. Dissertation, University of South Carolina (2020). Abstract (A050249, A076336, A125001)
  98. C. A. Souza-Filho, A. F. Macedo-Junior, A. M. S. Macedo, A hypergeometric generating function approach to charge counting statistics in ballistic chaotic cavities, J. Phys. A: Math. Theor. 47 (2014); 105102 doi:10.1088/1751-8113/47/10/105102.
  99. Yüksel Soykan, Gaussian Generalized Tetranacci Numbers, arXiv:1902.03936 [math.NT], 2019. (A000078, A073817)
  100. Yüksel Soykan, Tetranacci and Tetranacci-Lucas Quaternions, arXiv:1902.05868 [math.RA], 2019. (A000078, A073817)
  101. Yüksel Soykan, On Generalized Pentanacci and Gaussian Generalized Pentanacci Numbers, Preprints (2019). doi:10.20944/preprints201906.0110.v1 (A001591)
  102. Yüksel Soykan, Matrix Sequences of Tetranacci and Tetranacci-Lucas Numbers, Zonguldak Bülent Ecevit University (Zonguldak, Turkey), Preprints (2019), 2019070205. doi:10.20944/preprints201907.0205.v1 (A000078, A073817)
  103. Yüksel Soykan, On A Generalized Pentanacci Sequence, Asian Research Journal of Mathematics (2019) Vol. 14, No. 3, 1-9. doi:10.9734/ARJOM/2019/v14i330129 (A001591, A074048)
  104. Yüksel Soykan, On Generalized Third-Order Pell Numbers, Asian Journal of Advanced Research and Reports (2019) Vol. 6, No. 1, Article No. AJARR.51635, 1-18. doi:10.9734/AJARR/2019/v6i130144 (A000129, A077939, A077997, A276225)
  105. Yüksel Soykan, Summing Formulas For Generalized Tribonacci Numbers, arXiv:1910.03490 [math.GM], 2019. (A000073, A000931, A001608, A001644, A057597, A066983, A072328, A073145, A077939, A077947, A077978, A077997, A078012, A078049, A078712, A128587, A159284, A176971, A226308, A276225, A276228)
  106. Yüksel Soykan, On Summing Formulas For Generalized Fibonacci and Gaussian Generalized Fibonacci Numbers, Advances in Research (2019) Vol. 20, No. 2, 1-15, Article AIR.51824. doi:10.9734/AIR/2019/v20i230154 (A000032, A000045, A000129, A001045, A002203, A014551)
  107. Yüksel Soykan, A Study of Generalized Fourth-Order Pell Sequences, Journal of Scientific Research & Reports (2019) Vol. 25, No. 1, 1-18, Article No. JSRR.52074. doi:10.9734/JSRR/2019/v25i1-230177 (A103142, A190139, A331413)
  108. Yüksel Soykan, On Hyperbolic Numbers With Generalized Fibonacci Numbers Components, Zonguldak Bülent Ecevit University (Turkey, 2019). doi:10.13140/RG.2.2.19903.87207 (A000032, A000045)
  109. Yüksel Soykan, Summation Formulas for Generalized Tetranacci Numbers, Asian Journal of Advanced Research and Reports (2019) Vol. 7, No. 2, Article No. AJARR.52434, 1-12. doi:10.9734/AJARR/2019/v7i230170 (A000078, A073817, A103142, A226309)
  110. Yüksel Soykan, Sum Formulas for Generalized Fifth-Order Linear Recurrence Sequences, Journal of Advances in Mathematics and Computer Science (2019) Vol. 34, No. 5, 1-14. doi:10.9734/JAMCS/2019/v34i530224 (A001591, A074048, A141488, A226310, A226311)
  111. Yüksel Soykan, On generalized sixth-order Pell sequences, Journal of Scientific Perspectives (2020) Vol. 4, No. 1, 49-70. doi:10.26900/jsp.4.005 (A000129)
  112. Yüksel Soykan, Generalized Fibonacci Numbers: Sum Formulas, Journal of Advances in Mathematics and Computer Science (2020) Vol. 35, No. 1, 89-104. doi:10.9734/jamcs/2020/v35i130241 (A000032, A000045, A000129, A001045, A002203, A014551)
  113. Yüksel Soykan, Closed Formulas for the Sums of Squares of Generalized Fibonacci Numbers, Asian Journal of Advanced Research and Reports (2020) Vol. 9, No. 1, 23-39, Article no. AJARR.55441. doi:10.9734/AJARR/2020/v9i130212 (A000032, A000045, A000129, A001045, A002203, A014551)
  114. Yüksel Soykan, Generalized Tribonacci Numbers: Summing Formulas, Int. J. Adv. Appl. Math. and Mech. (2020) Vol. 7, No. 3, 57–76. (A000073, A000931, A001608, A001644, A057597, A066983, A072328, A073145, A077939, A077947, A077978, A077997, A078012, A078049, A078712, A128587, A159284, A176971, A226308, A276225, A276228)
  115. Yüksel Soykan, On Generalized Narayana Numbers, Int. J. Adv. Appl. Math. and Mech. (2020) Vol. 7, No. 3, 43-56. (A000930, A001263, A001609, A078012)
  116. Yüksel Soykan, On Generalized Grahaml Numbers, Journal of Advances in Mathematics and Computer Science (2020) Vol. 35, No. 2: 42-57, Article no. JAMCS.55255. doi:10.9734/JAMCS/2020/v35i230248 (A335718, A335719, A335720)
  117. Yüksel Soykan, On Generalized 2-primes Numbers, Asian Journal of Advanced Research and Reports, (2020) Vol. 9, Issue 2, 34-53. doi:10.9734/ajarr/2020/v9i230217
  118. Yüksel Soykan, A Study On Sums of Cubes of Generalized Fibonacci Numbers: Closed Formulas of Sum_{k=0..n} xk Wk3 and Sum_{k=1..n} xk W−k3, Preprints (2020), 2020040437. doi:10.20944/preprints202004.0437.v1 (A000032, A000045, A000129, A001405, A002203, A014551)
  119. Yüksel Soykan, On the Sums of Squares of Generalized Tribonacci Numbers: Closed Formulas of Sum_{k=0..n} xk Wk², Archives of Current Research International (2020) Vol. 20, Issue 4, Article no.ACRI.57840, 22-47. doi:10.9734/ACRI/2020/v20i430187 (A000073, A000931, A001608, A001609, A001644, A057597, A066983, A072328, A073145, A077939, A077947, A077978, A077997, A078012, A078049, A128587, A159284, A176971, A226308, A276225, A276228)
  120. Yüksel Soykan, A Study on Generalized Fibonacci Numbers: Sum Formulas Sum_{k=0..n} kxk Wk3 and Sum_{k=1..n} kxk W−k3 for the Cubes of Terms, Earthline Journal of Mathematical Sciences (2020) Vol. 4, No. 2, 297-331. doi:10.34198/ejms.4220.297331 (A000032, A000045, A000129, A001045, A002203, A014551)
  121. Yüksel Soykan, Generalized Pell-Padovan Numbers, Asian Journal of Advanced Research and Reports (2020) Vol. 11, No. 2, 8-28, Article No. 57839. doi:10.9734/AJARR/2020/v11i230259 (A008346, A066983, A099925)
  122. Yüksel Soykan, On Sum Formulas for Generalized Tribonacci Sequence, Journal of Scientific Research and Reports (2020) Vol. 26, Issue 7. doi:10.9734/jsrr/2020/v26i730283
  123. Yüksel Soykan, Properties of Generalized 6-primes Numbers, Archives of Current Research International (2020) Vol. 20, No. 6, 12-30, Article No. ACRI.60386. doi:10.9734/ACRI/2020/v20i630199
  124. Yüksel Soykan, Properties of Generalized (r, s, t, u)-Numbers, Earthline J. of Math. Sci. (2021) Vol. 5, No. 2, 297-327. doi:10.34198/ejms.5221.297327 (A000078, A007907, A073817, A103142, A190139, A226309, A331413)
  125. Yüksel Soykan, On Generalized (r, s)-numbers, Int. J. Adv. Appl. Math. and Mech. (2020) Vol. 8, No. 1, 1–14. (A000045, A000032, A000129, A001045, A002203, A014551)
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  283. Jeremy G. Sumner, Michael D. Woodhams, Lie-Markov models derived from finite semigroups, arXiv:1709.00520 [math.GR], 2017.
  284. Brian Y. Sun, Baoyindureng Wu, Two-log-convexity of the Catalan-Larcombe-French sequence, Journal of Inequalities and Applications, 2015, 2015:404; doi:10.1186/s13660-015-0920-0.
  285. Brian Y. Sun, JX Meng, Proof of a Conjecture of Z.-W. Sun on Trigonometric Series, arXiv preprint arXiv:1606.08153, 2016
  286. Ping Sun, Enumeration of standard Young tableaux of shifted strips with constant width, arXiv preprint arXiv:1506.07256, 2015 Also Electronic Journal of Combinatorics, Volume 24(2), 2017, #P2.41.
  287. Ping Sun, Enumeration formulas for standard Young tableaux of nearly hollow rectangular shapes, Discrete Mathematics, 341 (2018), 1144-1149. doi:10.1016/j.disc.2017.10.005
  288. Qifu Tyler Sun, Hanqi Tang, Zongpeng Li, Xiaolong Yang, Keping Long, Circular-shift Linear Network Codes with Arbitrary Odd Block Lengths, arXiv:1806.04635 [cs.IT], 2018. (A001122)
  289. Xinyu Sun, "New Lower Bound On The Number of Ternary Square-Free Words", J. Integer Sequences, Volume 6, 2003, Article 03.3.2.
  290. Yidong Sun, The Star of David Rule (2008); arXiv:0805.1277; Linear Algebra and its Applications, Volume 429, Issues 8-9, 16 October 2008, Pages 1954-1961.
  291. Yidong Sun and Fei Ma, Four transformations on the Catalan triangle, arXiv preprint arXiv:1305.2017, 2013
  292. Yidong Sun and Fei Ma, Minors of a Class of Riordan Arrays Related to Weighted Partial Motzkin Paths, arXiv preprint arXiv:1305.2015, 2013
  293. Yidong Sun and Fei Ma, Some new binomial sums related to the Catalan triangle, Electronic Journal of Combinatorics 21(1) (2014), #P1.33
  294. Sun, Yidong; Ma, Luping doi:10.1016/j.ejc.2014.01.004 Minors of a class of Riordan arrays related to weighted partial Motzkin paths. Eur. J. Comb. 39, 157-169 (2014).
  295. Yidong Sun and Zhiping Wang, Pattern Avoidance in Generalized Non-crossing Trees (2008); arXiv:0805.1280
  296. Yidong Sun and Zhiping Wang, String pattern avoidance in generalized non-crossing trees, Disc. Math. Theor. Comp. Sci. 11 (2009) 79-94.
  297. Sun, Yidong; Wu, Xiaojuan The largest singletons of set partitions. European J. Combin. 32 (2011), no. 3, 369-382.
  298. Sun, Yidong; Xu, Yanjie The largest singletons in weighted set partitions and its applications. Discrete Math. Theor. Comput. Sci. 13 (2011), no. 3, 75-85.
  299. Yidong Sun, Liting Zhai, Some properties of a class of refined Eulerian polynomials, arXiv:1810.07956 [math.CO], 2018. (A000111, A008292)
  300. Zhe Sun, T Suenaga, P Sarkar, S Sato, M Kotani, H Isobe, Stereoisomerism, crystal structures, and dynamics of belt-shaped cyclonaphthylenes, Proc. Nath. Acead. Sci. USA, vol. 113 no. 29, pp. 8109–8114, doi:10.1073/pnas.1606530113
  301. Zhi-Hong Sun, "Expansion and identities concerning Lucas Sequences", The Fibonacci Quarterly, Volume 44, May 2006, pages 145-153.
  302. Sun, Zhi-Hong Congruences concerning Lucas sequences. Int. J. Number Theory 10 (2014), no. 3, 793-815.
  303. Zhi-Hong Sun, Congruences for Domb and Almkvist-Zudilin numbers, Integral Transforms & Special Functions, Vol. 26 Issue 8, p642-659, 2015, doi:10.1080/10652469.2015.1034122
  304. Zhi-Hong Sun, Supercongruences involving Euler polynomials, Proc. American Mathematical Society, 144 (2016), 3295-3308.
  305. Zhi-Hong Sun, Congruences for Apéry-like numbers, arXiv:1803.10051 [math.NT], 2018. (A000172, A002825, A002893, A005258, A005259, A053175, A093388, A125143, A290575, A291898).
  306. Zhi-Hong Sun, Super congruences concerning binomial coefficients and Apéry-like numbers, arXiv:2002.12072 [math.NT], 2020. (A002895, A125143, A291898)
  307. Zhi-Wei Sun, doi:10.1016/j.jnt.2011.06.005 On Delannoy numbers and Schroeder numbers, J. Number Theory 131 (2011) 2387-2397; arXiv:1009.2486.
  308. Zhi-Wei Sun, On sums involving products of three binomial coefficients, arXiv:1012.3141 and Acta Arith. 156 (2) (2012) 123-141 doi:10.4064/aa156-2-2
  309. Sun, Zhi-Wei, p-adic valuations of some sums of multinomial coefficients. Acta Arith. 148 (2011), no. 1, 63-76.
  310. Z.-W. Sun, Conjectures involving arithmetical sequences, Number Theory: Arithmetic in Shangrila (eds., S. Kanemitsu, H.-Z. Li and J.-Y. Liu), Proc. the 6th China-Japan Sem. Number Theory (Shanghai, August 15-17, 2011), World Sci., Singapore, 2013, pp. 244-258; PDF.
  311. Zhi-Wei Sun, Conjectures involving combinatorial sequences, Arxiv preprint arXiv:1208.2683, 2012
  312. Zhi-Wei Sun, On sums of Apery polynomials and related congruences. J. Number Theory 132 (2012) 2673-2699 doi:10.1016/j.jnt.2012.05.014
  313. Z.-W. Sun, Conjectures involving primes and quadratic forms, arXiv preprint arXiv:1211.1588, 2012
  314. Zhi-Wei Sun, Products and Sums Divisible by Central Binomial Coefficients, Electronic Journal of Combinatorics, 20(1) (2013), #P9.
  315. Z.-W. Sun, Fibonacci numbers modulo cubes of primes, arXiv:0911.3060; Taiwanese J. Math. 17 (2013). doi:10.11650/tjm.17.2013.2488
  316. Z.-W. Sun, Connections between p = x^2+ 3y^2 and Franel numbers, J. Number Theory 133 (2013), no. 9, 2914-2928.
  317. Z.-W. Sun On some determinants with Legendre symbol entries, 2013; PDF
  318. Z.-W. Sun, Some new problems in additive combinatorics, arXiv preprint arXiv:1309.1679, 2013
  319. Z.-W. Sun, On a^n+ bn modulo m, arXiv preprint arXiv:1312.1166, 2013
  320. ZW SUN, A conjecture on unit fractions involving primes, Preprint 2015;
  321. Sun, Zhi-Wei On functions taking only prime values. J. Number Theory 133 (2013), no. 8, 2794-2812.
  322. Sun, Zhi-Wei Congruences for Franel numbers. Adv. in Appl. Math. 51 (2013), no. 4, 524-535.
  323. Z.-W. Sun, Problems on combinatorial properties of primes, arXiv preprint arXiv:1402.6641, 2014
  324. Z.-W. Sun, New observations on primitive roots modulo primes, arXiv preprint arXiv:1405.0290, 2014
  325. Z.-W. Sun, Congruences involving g_n(x) = Sum_{k= 0..n} C(n,k)^2 C(2k,k) x^k, arXiv preprint arXiv:1407.0967, 2014
  326. Sun, Zhi-Wei Congruences involving generalized central trinomial coefficients. Sci. China Math. 57 (2014), no. 7, 1375-1400.
  327. Z.-W. Sun, A result similar to Lagrange's theorem, arXiv preprint arXiv:1503.03743, 2015
  328. Zhi-Wei Sun, Refining Lagrange's four-square theorem, arXiv:1604.06723, 2016.
  329. Zhi-Wei Sun, Conjectures on representations involving primes, In: M. Nathanson (ed.), Combinatorial and Additive Number Theory II: CANT, New York, NY, USA, 2015 and 2016, Springer Proc. in Math. & Stat., Vol. 220, Springer, New York, 2017, pp. 279-310;
  330. Zhi-Wei Sun, Some new series for 1/π motivated by congruences, arXiv:2009.04379 [math.NT], 2020. (A337247, A337332 in references)
  331. Zhi-Wei Sun, New Conjectures of Representations of Integers (I), Nanjing Univ. J. Math. Biquarterly 34 (2017), No. 2, 97-120. [PDF]. (A260418, A262827, A266152, A266153, A266212, A266215, A266230, A266231, A266277, A266314, A266363, A266364, A266528, A266548, A266985, A267861, A271076, A271099, A271169, A271237, A275150, A280153, A280356, A290491)
  332. Zhi-Wei Sun, Quadratic residues and related permutations and identities, arXiv:1809.07766 [math.NT], 2018. (A319311, A319882, A319894, A319903, A320044)
  333. Zhi-Wei Sun, On permutations of {1, ..., n} and related topics, arXiv:1811.10503 [math.CO], 2018. (A073112, A073364, A126972, A321597, A321610, A321611, A321727, A322069, A322070, A322099, A322363)
  334. Zhi-Wei Sun, On some determinants with Legendre symbol entries, Finite Fields and Their Applications (2019) Vol. 56, 285-307. doi:10.1016/j.ffa.2018.12.004
  335. Zhi-Wei Sun, On some determinants involving the tangent function, arXiv:1901.04837 [math.NT], 2019. (A277445)
  336. Zhi-Wei Sun, Riddles of Representations of Integers, presentation to Nanjing Normal Univ. (China, 2019). PDF (A286944)
  337. Zhi-Wei Sun, Sums of four squares with certain restrictions, arXiv:2010.05775 [math.NT], 2020. (A335624, A337082, A338019, A338094, A338095, A338096, A338103, A338119, A338121, A338139)
  338. Zhi-Wei Sun and Roberto Tauraso, Congruences involving Catalan numbers (2007), arXiv:0709.1665.
  339. Z-W. Sun and R. Tauraso, doi:10.1016/j.aam.2010.01.001 New congruences for central binomial coefficients, Adv. Appl Math 45 (1) (2010) 125-148
  340. Sun, Zhi-Wei; Tauraso, Roberto On some new congruences for binomial coefficients. Int. J. Number Theory 7 (2011), no. 3, 645-662.
  341. Zhi-Wei Sun, Lilu Zhao, On the set {π(k n): k = 1, 2, 3, …}, arXiv:2004.01080 [math.NT], 2020. (A237578)
  342. Sheila Sundaram, On a positivity conjecture in the character table of S_n, arXiv:1808.01416 [math.CO], 2018. (A046682)
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  345. Z. Sunik [or Sunic], Self-describing sequences and the Catalan family tree (PostScript , Pdf), Electron. J. Combin. 10 (2003), Note 5, 9 pp.
  346. Zoran Sunik [or Sunic], Tree morphisms, transducers and integer sequences (2006), arXiv:math/0612080.
  347. Zoran Sunik [or Sunic], "Rational Tree Morphisms and Transducer Integer Sequences: Definition and Examples", J. Integer Sequences, Volume 10, 2007, Article 07.4.3.
  348. Asep K. Supriatna, Ema Carnia, Meksianis Z. Ndii, Fibonacci numbers: A population dynamics perspective, Heliyon (2019) Vol. 5, Issue 1, e01130. doi:10.1016/j.heliyon.2019.e01130 (A000045)
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