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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]

"We found the formulas for the coefficients in Proposition 11 thanks to OEIS database." [Stefan Barańczuk, 2019]

"We encourage anyone pursuing these problems to make good use of the OEIS, as we were frequently (pleasantly) surprised at the myriad connections to other areas of combinatorics." [V. Bardenova et al., 2022]

"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]

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  • Works are arranged in alphabetical order by author's last name.
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  • 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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References

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  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.
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  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
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  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; http://140.109.74.92/hk/wp-content/files/2016/03/rand-perm-2016-v1.pdf
  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 https://hal.archives-ouvertes.fr/hal-01025881v3, 2015. Elec. J. Combinat. 22 (4) (2015) P4.40 doi:10.37236/5183
  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; https://hal.archives-ouvertes.fr/hal-01503749v1 (only version 1 refers to the OEIS)
  38. Roland Bacher, Generic numerical semigroups, hal-03221466 [math.CO], 2021. Abstract (A003116, A008930)
  39. Roland Bacher, Yet another Proof of an old Hat, arXiv:2111.02788 [math.HO], 2021. (A349005)
  40. Roland Bacher and P De La Harpe, Conjugacy growth series of some infinitely generated groups. 2016. hal-01285685v2; https://hal.archives-ouvertes.fr/hal-01285685/document
  41. Roland Bacher and Philippe Flajolet, Pseudo-factorials, elliptic functions, and continued fractions (2009) arXiv:0901.1379 and Ramanujan J. 21 (1) (2010) 71-97 doi:doi.org/10.1007/s11139-009-9186-9
  42. R. Bacher and D. Garber, arXiv:math.GT/0205245 Spindle configurations of skew lines, Geom. Topol. 11 (2007), 1049-1081.
  43. Bacher, R.; Krattenthaler, C. Chromatic statistics for triangulations and Fuß-Catalan complexes. Electron. J. Combin. 18 (2011), no. 1, Paper 152, 16 pp.
  44. 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.
  45. R Bacher, C Reutenauer, Number of right ideals and a q-analogue of indecomposable permutations, arXiv preprint arXiv:1511.00426, 2015
  46. Bacher, Roland and Schaeffer, Gilles, On generating series of coloured planar trees. Sém. Lothar. Combin. 55 (2005/06), Art. B55e, 20 pp.
  47. R. Bacher and C. Krattenthaler, Chromatic statistics for triangulations and FussCatalan complexes, Electronic Journal of Combinatorics, 18 (2011), #P152.
  48. Rolf Bachmann, Marcel Klinger, and Jan Meyer, Random Branching and Crosslinking of Polymer Chains, Analytical Functions for the Bivariate Molecular Weight Distributions, Macromolecular Theory and Simulations (2022) 2200062. doi:10.1002/mats.202200062
  49. J Backelin, Sizes of the extremal girth 5 graphs of orders from 40 to 49, arXiv preprint arXiv:1511.08128, 2015
  50. 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
  51. Dave Bacon, Andrew M. Childs, Wim van Dam, Optimal measurements for the dihedral hidden subgroup problem (2005), arXiv:quant-ph/0501044.
  52. 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.
  53. 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)
  54. 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.
  55. 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
  56. G. Badkobeh, G. Fici, Sz. Liptak, On the number of closed factors in a word, arXiv:1305.6395, doi:10.1007/978-3-319-15579-1_29
  57. Dzmitry Badziahin, Jeffrey Shallit, An Unusual Continued Fraction, preprint arXiv:1505.00667, 2015 (A006519, A100338, A100865, A100864)
  58. Sunghan Bae, Su Hu, Min Sha, On the Carmichael rings, Carmichael ideals and Carmichael polynomials, arXiv:1809.05432 [math.NT], 2018. (A002997)
  59. HUNKI BAEK, SEJEONG BANG, DONGSEOK KIM, AND JAEUN LEE, A bijection between aperiodic palindromes and connected circulant graphs, arXiv:1412.2426, 2014
  60. 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)
  61. 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.]
  62. O. Bagdasar, On certain computational and geometric properties of complex Horadam orbits, ANTS 2014, https://ants2014.kookmin.ac.kr/ANTS_2014_poster_Bagdasar.pdf
  63. 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
  64. Ovidiu Bagdasar, Dorin Andrica, A new formula for the coefficients of Gaussian polynomials, Analele Stiintifice ale Universitatii Ovidius Constanta (2019). Abstract
  65. 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)
  66. O. D. Bagdasar and P. J. Larcombe, On the number of complex Horodam sequences ..., Fib. Q., 51 (2013), 339-347.
  67. Ovidiu D. Bagdasar and Larcombe, Peter J., "On the masked periodicity of Horadam sequences: a generator-based approach", Fib. Q., 55 (2017), 332-339
  68. 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
  69. 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)
  70. 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)
  71. 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
  72. Marco Baggio, Vasilis Niarchos, Kyriakos Papadodimas, Gideon Vos, Large-N correlation functions in N = 2 superconformal QCD, arXiv preprint arXiv:1610.07612, 2016
  73. Aaron R. Bagheri, Classifying the Jacobian Groups of Adinkras, (2017), HMC Senior Theses.
  74. Fatemeh Bagherzadeh and Murray Bremner, Commutativity in double interchange semigroups, arXiv:1706.04693 [math.RA], 2017.
  75. Fatemeh Bagherzadeh, M Bremner, S Madariaga, Jordan Trialgebras and Post-Jordan Algebras, arXiv preprint arXiv:1611.01214, 2016.
  76. Eli Bagno, Riccardo Biagioli, and David Garber, Some identities involving second kind Stirling numbers of types B and D, arXiv:1901.07830 [math.CO], 2019. (A039755, A039760, A143395)
  77. Eli Bagno, Estrella Eisenberg, Shulamit Reches, and Moriah Sigron, On the poset of King-Non-Attacking permutations, arXiv:1905.02387 [math.CO], 2019. (A002464)
  78. Eli Bagno, Estrella Eisenberg, Shulamit Reches, and Moriah Sigron, Separators - a new statistic for permutations, arXiv:1905.12364 [math.CO], 2019. (A137774)
  79. Eli Bagno, Estrella Eisenberg, Shulamit Reches, and Moriah Sigron, Counting King Permutations on the Cylinder, arXiv:2001.02948 [math.CO], 2020. (A002464, A002493)
  80. Eli Bagno, Estrella Eisenberg, Shulamit Reches, and Moriah Sigron, On the Sparseness of the Downsets of Permutations via Their Number of Separators, Enumerative Combinatorics and Applications (2021) Vol. 1, No. 3, Article #S2R21. PDF (A137774)
  81. Eli Bagno, Estrella Eisenberg, Shulamit Reches, and Moriah Sigron, Blockwise simple permutations, arXiv:2303.13115 [math.CO], 2023. (A054514, A054515, A059372)
  82. Eli Bagno and David Garber, Signed partitions - A balls into urns approach, arXiv:1903.02877 [math.CO], 2019. (A039755, A143395)
  83. Eli Bagno and David Garber, Combinatorics of q,r-analogues of Stirling numbers of type B, arXiv:2401.08365 [math.CO], 2024. (A085483, A132393, A143395)
  84. Eli Bagno and David Garber, Mordechai Novick, The Worpitzky identity for the groups of signed and even-signed permutations, arXiv:2004.03681 [math.CO], 2020. (A060187, A262226)
  85. Maryam Bahrani and Jérémie Lumbroso, Enumerations, Forbidden Subgraph Characterizations, and the Split-Decomposition, arXiv:1608.01465, 2016.
  86. 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
  87. James Haoyu Bai, Joseph Meleshko, Samin Riasat, and Jeffrey Shallit, Quotients of Palindromic and Antipalindromic Numbers, arXiv:2202.13694 [math.NT], 2022. (A006995, A035928, A305468, A305469, A305470, A351172, A351173)
  88. P. A. Baikov and S. V. Mikhailov, The {β}-expansion for Adler function, Bjorken Sum Rule, and the Crewther-Broadhurst-Kataev relation at order O(αs⁴), J. High Energy Phys. 09 (2022) Art. No. 185. doi:10.1007/JHEP09(2022)185 see also arXiv:2206.14063 [hep-ph], 2022. (A000070)
  89. Alex Bailey, Martin Finn-Sell, Robert Snocken, Subsemigroup, ideal and congruence growth of free semigroups, arXiv preprint arXiv:1409.2444, 2014
  90. BENJAMIN BAILY, JUSTINE DELL, HENRY L. FLEISCHMANN, FAYE JACKSON, STEVEN J. MILLER, ETHAN PESIKOFF, AND LUKE REIFENBERG, IRREDUCIBILITY OVER THE MAX-MIN SEMIRING, arXiv, to appear 2021.
  91. D. H. Bailey, Book Reviews, Math. Comp. 65 (1996), 877-895.
  92. D. H. Bailey, Compendium to BBP formulas
  93. 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].
  94. D. H. Bailey and J. M. Borwein, Experimental mathematics: examples, methods and implications, Notices Amer. Math. Soc. 52 (2005), 502-514.
  95. David H. Bailey and Jonathan M. Borwein, Exploratory Experimentation and Computation, Notices of the AMS, 58 (No. 10, 2011), 1410-1419; http://www.ams.org/notices/201110/rtx111001410p.pdf.
  96. 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; http://moodle.thecarma.net/jon/ontology.pdf
  97. 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."
  98. 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; https://carmamaths.org/resources/jon/ICERM-2014.pdf
  99. D. H. Bailey, J. M. Borwein, J. S. Kimberley, Discovery of large Poisson polynomials using the MPFUN-MPFR arbitrary precision software, Preprint 2015; http://www.davidhbailey.com/dhbpapers/poisson-res.pdf
  100. R. A. Bailey and P. J. Cameron, Latin squares: Equivalents and equivalence, Draft, May 2003.
  101. Scott M. Bailey and Donald M. Larson, The A(1)-module structure of the homology of Brown-Gitler spectra, arXiv:2107.01316 [math.AT], 2021. (A000123, A018819, A131025)
  102. R. Baillie, Fun With Very Large Numbers, arXiv:1105.3943, 2011
  103. Robert Baillie, Wright's Fourth Prime, arXiv:1705.09741 [math.NT], 2017.
  104. R. Baillie, D. Borwein and J. M. Borwein, Surprising sync sums and integrals, Amer. Math. Monthly, 115 (2008), 888-901.
  105. Reginald Bain, A Musical Scale Generated from the Ratio of Consecutive Primes, Proceedings of Bridges 2015: Mathematics, Music, Art, Architecture, Culture, http://m.archive.bridgesmathart.org/2015/bridges2015-407.pdf
  106. W. D. Baird, Cops and robbers on graphs and hypergraphs, MS Thesis, Applied Mathematics, Ryerson University, 2011.
  107. 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.
  108. 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)
  109. GN Bakare, SO Makanjuola, Some Results on Properties of Alternating Semigroups, Nigerian Journal of Mathematics and Applications Volume 24,(2015), 184−192; http://www.kwsman.com
  110. 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)
  111. Breeanne Baker Swart, Susan Crook, Helen G. Grundman, Laura Hall-Seelig, Gaussian Happy Numbers, arXiv:2101.00560 [math.NT], 2021. (A007770)
  112. 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)
  113. Zachary Baker, Properties and Calculations of Constructive Orderings of Z/nZ, Minnesota J. of Undergrad. Math. (2018-2019) Vol. 4, No. 1, see p. 9. Abstract (A141599)
  114. 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.
  115. Valentin Bakoev, Algorithmic approach to counting certain types of m-ary partitions, Discrete Mathematics, Vol 275 (2004), pp. 17-41.
  116. Valentin P. Bakoev, The recurrence relations in teaching students of informatics, Inf. in Educ. 9 (2010) 159-170.
  117. Valentin Bakoev, Ordinances of the vectors of the n-dimensional Boolean cube in accordance with their weights. PDF (A294648)
  118. Valentin Bakoev, Combinatorial and Algorithmic Properties of One Matrix Structure at Monotone Boolean Functions, arXiv:1902.06110 [cs.DM], 2019. (A000372)
  119. Valentin Bakoev, Fast Computing the Algebraic Degree of Boolean Functions, arXiv:1905.08649 [cs.DM], 2019. (A051459, A294648, A305860, A319511)
  120. Valentin Bakoev, Ordering the Boolean Cube Vectors by Their Weights and with Minimal Change, Int'l Conf. Algebraic Informatics (CAI 2022) Lecture Notes Comp. Sci. (LNCS) Vol. 13706, 43–54. doi:10.1007/978-3-031-19685-0_4 (A351939)
  121. Hartosh Singh Bal, Combinatorics of a Class of Completely Additive Arithmetic Functions, arXiv:2308.00455 [math.CO], 2023. (A006645, A115593)
  122. 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)
  123. Félix Balado and Guénolé C.M. Silvestre, Runs of Ones in Binary Strings, arXiv:2302.11532 [math.CO], 2023. (A001792, A045623)
  124. Srivatsan Balakrishnan, Suresh Govindarajan and Naveen S. Prabhakar, On the asymptotics of higher-dimensional partitions, arXiv:1105.6231.
  125. 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.
  126. 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
  127. Krishnan Balasubramanian, Topological Indices, Graph Spectra, Entropies, Laplacians, and Matching Polynomials of n-Dimensional Hypercubes, Symmetry (2023) Vol. 15, No. 2, 557. doi:10.3390/sym15020557 (A192437)
  128. Krishnan Balasubramanian and Ramon Carbó-Dorca, Three Conjectures on Extended Twin Primes and the Existence of Isoboolean and Singular Primes Inspired by Relativistic Quantum Computing, Arizona State Univ. (2022). PDF (A000602)
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  278. Gill Barequet, Gil Ben-Shachar, and Martha Carolina Osegueda, Applications of Concatenation Arguments to Polyominoes and Polycubes, EuroCG '20, 36th European Workshop on Computational Geometry, (Würzburg, Germany, 16-18 March 2020). PDF See also Computational Geometry (October 2021) Vol. 98, 101790. doi:10.1016/j.comgeo.2021.101790 (A001168, A001931, A066158, A118356, A151830, A151831, A151832, A151833, A151834, A151835, A191094, A191095, A191096, A191097, A191098)
  279. Gill Barequet, Solomon W. Golomb, and David A. Klarner, Polyominoes. (This is a revision, by G. Barequet, of the chapter of the same title originally written by the late D. A. Klarner for the first edition, and revised by the late S. W. Golomb for the second edition.) Preprint, 2016, http://www.csun.edu/~ctoth/Handbook/chap14.pdf
  280. Gill Barequet and Bar Magal, Automatic generation of formulae for polyominoes with a fixed perimeter defect, Comp. Geom. (2022) 101919. doi:10.1016/j.comgeo.2022.101919
  281. Gill Barequet, Günter Rote, Mira Shalah, An improved upper bound on the growth constant of polyiamonds, Preliminary version: proceedings of the 32nd European workshop on computational geometry (2019, Lugano, Switzerland), Acta Math. Univ. Comenianae. PDF (A001420)
  282. G. Barequet, M. Shalah, Automatic Proofs for Formulae Enumerating Proper Polycubes, 31st International Symposium on Computational Geometry (SoCG’15). Editors: Lars Arge and János Pach; pp. 19–22, 2015.
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  284. Gill Barequet, Mira Shalah, Counting n-cell polycubes proper in n - k dimensions, European Journal of Combinatorics, Volume 63, June 2017, p. 146-163. doi:10.1016/j.ejc.2017.03.006
  285. Gill Barequet, Mira Shalah, Yufei Zheng, An Improved Lower Bound on the Growth Constant of Polyiamonds, In: Cao Y., Chen J. (eds) Computing and Combinatorics, COCOON 2017, Lecture Notes in Computer Science, vol 10392. doi:10.1007/978-3-319-62389-4_5
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  287. Alexander Barg, Stolarsky's invariance principle for finite metric spaces, arXiv:2005.12995 [math.CO], 2020. (A001803, A002420, A002424, A002457)
  288. Till Bargheer, Systematics of the Multi-Regge Three-Loop Symbol, arXiv:1606.07640 [hep-th]
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  290. JL Baril, Avoiding patterns in irreducible permutations, Discrete Mathematics and Theoretical Computer Science, submitted 2014.
  291. Sara Barrows, Emily Noye, Sarah Uttormark, and Matthew Wright, Three's A Crowd: An Exploration of Subprime Tribonacci Sequences, College Math. J. (2023). doi:10.1080/07468342.2023.2263109 (A214674)
  292. Jean-Luc Baril and Paul Barry, Two kinds of partial Motzkin paths with air pockets, arXiv:2212.12404 [math.CO], 2022. (A001006, A033184, A091836, A101499, A114465, A159771)
  293. Jean-Luc Baril, David Bevan, Sergey Kirgizov, Bijections between directed animals, multisets and Grand-Dyck paths, arXiv:1906.11870 [math.CO], 2019. (A000108, A001006, A001700, A005773)
  294. Jean-Luc Baril, Alexander Burstein, and Sergey Kirgizov, Pattern statistics in faro words and permutations, arXiv:2010.06270 [math.CO], 2020. (A000108, A001045, A001700, A006918, A047749, A107373, A124428, A212964, A340567, A340568)
  295. Jean-Luc Baril, Daniela Colmenares, José L. Ramírez, Emmanuel D. Silva, Lina M. Simbaqueba, and Diana A. Toquica, Consecutive pattern-avoidance in Catalan words according to the last symbol, Univ. Bourgogne (France 2023). PDF (A061639, A097609, A101499, A105633, A114465, A157003, A159769)
  296. JL Baril, R Genestier, A Giorgetti, A Petrossian, Rooted planar maps modulo some patternss, Preprint 2016; http://jl.baril.u-bourgogne.fr/cartes.pdf
  297. Jean-Luc Baril, Richard Genestier, Sergey Kirgizov, Pattern distributions in Dyck paths with a first return decomposition constrained by height, arXiv:1911.03119 [math.CO], 2019. (A025566, A025567, A097861, A304011)
  298. Jean-Luc Baril, Javier F. González, and José L. Ramírez, Last symbol distribution in pattern avoiding Catalan words, Université de Bourgogne (France, 2022). PDF (A007318, A055248, A105306, A155038)
  299. Jean-Luc Baril, Nathanaël Hassler, Sergey Kirgizov, and José L. Ramírez, Grand zigzag knight's paths, arXiv:2402.04851 [math.CO], 2024. (A000108, A002605, A051286, A052535, A096608, A128588, A158943, A182879)
  300. Jean-Luc Baril, Pamela E. Harris, Kimberly J. Harry, Matt McClinton, and José L. Ramírez, Enumerating runs, valleys, and peaks in Catalan words, arXiv:2404.05672 [math.CO], 2024. (A000984, A001263, A001700, A051924, A057552, A091894, A114492, A114502, A116424)
  301. J.-L. Baril, C. Khalil, V. Vajnovszki, Catalan and Schröder permutations sortable by two restricted stacks, arXiv:2004.01812 [cs.DM], 2020. (A000108, A006318)
  302. JL Baril, S Kirgizov, The pure descent statistic on permutations, Preprint, 2016, http://jl.baril.u-bourgogne.fr/Stirling.pdf
  303. Jean-Luc Baril and Sergey Kirgizov, Transformation à la Foata for special kinds of descents and excedances, arXiv:2101.01928 [math.CO], 2021. (A001705, A132393, A136394)
  304. Jean-Luc Baril and Sergey Kirgizov, Bijections from Dyck and Motzkin meanders with catastrophes to pattern avoiding Dyck paths, Disc. Math. Lett. (2021) Vol. 7, 5–10. doi:10.47443/dml.2021.0032 (A000108, A001006, A054391, A224747, A274115)
  305. Jean-Luc Baril, Sergey Kirgizov, Rémi Maréchal, and Vincent Vajnovszki, Grand Dyck paths with air pockets, arXiv:2211.04914 [math.CO], 2022. (A004148, A051286, A093128, A110236, A110320, A203611)
  306. Jean-Luc Baril, Sergey Kirgizov, and Mehdi Naima, A lattice on Dyck paths close to the Tamari lattice, arXiv:2309.00426 [math.CO], 2023. (A000108, A057552, A064062)
  307. Jean-Luc Baril, Sergey Kirgizov, Armen Petrossian, Dyck paths with a first return decomposition constrained by height, Submitted, 2017
  308. Jean-Luc Baril, Sergey Kirgizov, Armen Petrossian, Forests and pattern-avoiding permutations modulo pure descents, 2017.
  309. Jean-Luc Baril, Sergey Kirgizov, and Armen Petrossian, Dyck Paths with catastrophes modulo the positions of a given pattern, Univ. de Bourgogne Franche-Comté, 2022. PDF (A000045, A002054, A037952, A212804, A215004, A224747, A344191, A347493)
  310. Baril, Jean-Luc, Sergey Kirgizov, and Vincent Vajnovszki. "Patterns in treeshelves." Discrete Mathematics 340.12 (2017): 2946-2954; arXiv 1611.07793.
  311. Jean-Luc Baril, Sergey Kirgizov, Vincent Vajnovszki, Descent distribution on Catalan words avoiding a pattern of length at most three, arXiv:1803.06706 [math.CO], 2018. (A000108, A000124, A000217, A001519, A001787, A001793, A001870, A005183, A007051, A011782, A027471, A057960)
  312. Jean-Luc Baril, Sergey Kirgizov, Armen Petrossian, Enumeration of Łukasiewicz paths modulo some patterns, arXiv:1804.01293 [math.CO], 2018. (A000045, A000325, A001006, A001405, A004148, A005251, A011782, A023431, A165407, A191385, A292460, A302483)
  313. Jean-Luc Baril, Sergey Kirgizov, Armen Petrossian, Motzkin paths with a restricted first return decomposition, Integers (2019) Vol. 19, A46. Abstract (A000045, A000108, A000129, A001006, A002026, A026418, A097331)
  314. Jean-Luc Baril, Sergey Kirgizov, José L. Ramírez, and Diego Villamizar, The Combinatorics of Motzkin Polyominoes, arXiv:2401.06228 [math.CO], 2024. (A055217)
  315. J.-L. Baril, T. Mansour, A. Petrossian, Equivalence classes of permutations modulo excedances, 2014; http://jl.baril.u-bourgogne.fr/equival.pdf
  316. Jean-Luc Baril, Céline Moreira Dos Santos, Pizza-cutter's problem and Hamiltonian path, Mathematics Magazine (2019) Vol. 88, No. 1, 1-9. PDF (A000124, A090338)
  317. Baril, J.-L. and Pallo, J. M., The phagocyte lattice of Dyck words. Order 23 (2006), no. 2-3, 97-107.
  318. J.-L. Baril and J.M. Pallo, The pruning-grafting lattice of binary trees, Theoretical Computer Science, Volume 409, Issue 3, 28 December 2008, Pages 382-393.
  319. J.-L. Baril, J.-M. Pallo, Motzkin subposet and Motzkin geodesics in Tamari lattices, 2013; PDF, Inf. Process. Lett. 114 (2014) 31-37 doi:10.1016/j.ipl.2013.10.001
  320. Baril, Jean-Luc, and Jean-Marcel Pallo. "A Motzkin filter in the Tamari lattice." Discrete Mathematics 338.8 (2015): 1370-1378.
  321. J.-L. Baril, A. Petrossian, Equivalence classes of Dyck paths modulo some statistics, 2014; PDF. Baril, Jean-Luc; Petrossian, Armen. Equivalence classes of Dyck paths modulo some statistics. Discrete Math. 338 (2015), no. 4, 655--660. MR3300754
  322. Jean-Luc Baril, Armen Petrossian, Equivalence classes of permutations modulo descents and left-to-right maxima, preprint. (A001006, A000108, A000124, A000110)
  323. J.-L. Baril, A. Petrossian, Equivalence Classes of Motzkin Paths Modulo a Pattern of Length at Most Two, J. Int. Seq. 18 (2015) 15.7.1.
  324. Jean-Luc Baril, Helmut Prodinger, Enumeration of partial Lukasiewicz paths, arXiv:2205.01383 [math.CO], 2022. (A000012, A000079, A000108, A000245, A000344, A001519, A001906, A002057, A003462, A005021, A007051, A080937)
  325. Jean-Luc Baril and José L. Ramírez, Knight's paths towards Catalan numbers, Univ. Bourgogne Franche-Comté (2022). PDF (A000108, A004148, A005220, A005221, A088518, A096587, A096588, A111160, A166135, A187430, A210736)
  326. Jean-Luc Baril and José Luis Ramírez, Partial Motzkin paths with air pockets of the first kind avoiding peaks, valleys or double rises, arXiv:2301.10449 [math.CO], 2023. (A095980, A152171, A152225)
  327. Jean-Luc Baril and José Luis Ramírez, Descent distribution on Catalan words avoiding ordered pairs of Relations, arXiv:2302.12741 [math.CO], 2023. (A000027, A000045, A000124, A000129, A000217, A001006, A001787, A004148, A005775, A006645, A011782, A023610, A026418, A034867, A082582, A086615, A087626, A097894, A105633, A114690, A114711, A129710, A143013, A152225, A159771, A203019, A207538, A247333, A273717, A273718, A292460)
  328. Jean-Luc Baril and José L. Ramírez, Fibonacci and Catalan paths in a wall, 2023. PDF (A000045, A000108, A001006, A003440, A004148, A023610, A037952, A051286, A138156, A203611)
  329. Jean-Luc Baril, José L. Ramírez, and Lina M. Simbaqueba, Counting prefixes of skew Dyck paths, J. Int. Seq., Vol. 24 (2021), Article 21.8.2. HTML (A000108, A002212, A033321, A039598, A122737)
  330. J.-L. Baril, R. Vernay, Whole mirror duplication-random loss model and pattern avoiding permutations, Inf. Proc. Lett 110 (2010) 474-480 doi:10.1016/j.ipl.2010.04.016
  331. Daniel Barlet, Jón Magnússon, Complex Analytic Cycles I, Grundlehren der mathematischen Wissenschaften (GL, 2020) Vol. 356, Springer, Cham. doi:10.1007/978-3-030-31163-6
  332. Christoph Bärligea, On the dimension of the Fomin-Kirillov algebra and related algebras, arXiv:2001.04597 [math.QA], 2020. (A002464)
  333. Rupam Barman, Ajit Singh, On Mex-related partition functions of Andrews and Newman, arXiv:2009.11602 [math.NT], 2020. (A064428, A260894)
  334. Marilena Barnabei, Flavio Bonetti, and Niccolò Castronuovo, Motzkin and Catalan Tunnel Polynomials, J. Int. Seq., Vol. 21 (2018), Article 18.8.8. HTML (A000045, A000108, A001006, A001263, A006318, A097610, A097860, A098978, A114583, A129181, A132893, A138157, A181371)
  335. Marilena Barnabei, Flavio Bonetti, Niccolò Castronuovo, Matteo Silimbani, Consecutive patterns in restricted permutations and involutions, arXiv:1902.02213 [math.CO], 2019. (A107131, A114690, A129181)
  336. Marilena Barnabei, Flavio Bonetti, Niccolò Castronuovo, Matteo Silimbani, Ascending runs in permutations and valued Dyck paths, Ars Mathematica Contemporanea (2019) Vol. 16, No. 2, 445-463. doi:10.26493/1855-3974.1679.ad3 (A001003, A001586, A052709, A122045)
  337. Marilena Barnabei, Flavio Bonetti, Niccolò Castronuovo, Matteo Silimbani, Permutations avoiding a simsun pattern, The Electronic Journal of Combinatorics (2020) Vol. 27, Issue 3, P3.45. doi:10.37236/9482 (A000110, A000111, A001006, A005314, A105633, A152948)
  338. Marilena Barnabei, Flavio Bonetti, Niccolò Castronuovo, and Matteo Silimbani, Maxima and visibility in involutions, Adv. Appl. Math. (2023) Vol. 149, 102552. doi:10.1016/j.aam.2023.102552
  339. M. Barnabei, F. Bonetti, S. Elizalde, M. Silimbani, Descent sets on 321-avoiding involutions and hook decompositions of partitions, arXiv preprint arXiv:1401.3011, 2014
  340. Marilena Barnabei, Flavio Bonetti, Matteo Silimbani, Bijections and recurrences for integer partitions into a bounded number of parts, Applied Mathematics Letters, Volume 22, Issue 3, March 2009, Pages 297-303.
  341. M. Barnabei, F. Bonetti, and M. Silimbani, Restricted involutions and Motzkin paths (2008) arXiv:0812.0463 Adv. in Appl. Math. 47 (2011), no. 1, 102-115.
  342. M. Barnabei, F. Bonetti, and M. Silimbani, The distribution of consecutive patterns of length 3 in 3\textrm{-}1\textrm{-}2 -avoiding permutations (2009) arXiv:0904.0079 and Eur. J. Comb 31 (5) (2010) 1360-1371 doi:10.1016/j.ejc.2009.11.011
  343. M. Barnabei, F.Bonetti, and M. Silimbani, Combinatorial properties of the numbers of tableaux of bounded height (2008); arXiv:0803.2112
  344. Barnabei, Marilena; Bonetti, Flavio; and Silimbani, Matteo; The descent statistic on 123-avoiding permutations. Sem. Lothar. Combin. 63 (2010), Art. B63a, 8 pp.
  345. M. Barnabei, F. Bonetti and M. Silimbani, Two permutation classes related to the Bubble Sort operator, Electronic Journal of Combinatorics 19(3) (2012), #P25.
  346. M. Barnabei, F. Bonetti and M. Silimbani, Two permutation classes enumerated by the central binomial coefficients, arXiv preprint arXiv:1301.1790, 2013 and <a href="https://cs.uwaterloo.ca/journals/JIS/VOL16/Silimbani/silimbani3.html">J. Int. Seq. 16 (2013) #13.3.8</a>
  347. Tal Barnea, On the Riemann Zeta Function and the fractional part of rational powers, arXiv:1808.06653 [math.NT], 2018. (A013697)
  348. 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)
  349. George Barnes, Sanjaye Ramgoolam, and Michael Stephanou, Permutation invariant Gaussian matrix models for financial correlation matrices, arXiv:2306.04569 [q-fin.ST], 2023. (A050535)
  350. Barnes, Jeffrey M.; Benkart, Georgia; Halverson, Tom doi:10.1112/plms/pdv075 McKay centralizer algebras</a>. Proc. Lond. Math. Soc. (3) 112, No. 2, 375-414 (2016).
  351. Joel Barnes, Conformal welding of uniform random trees, Ph. D. Dissertation, Univ. Washington, 2014; https://dlib.lib.washington.edu/researchworks/bitstream/handle/1773/26116/Barnes_washington_0250E_13633.pdf?sequence=1&isAllowed=y
  352. M. P. Barnett, Some applications of high precision arithmetic
  353. Brandy Amanda Barnette, Counting Convex Sets on Products of Totally Ordered Sets, Masters Theses & Specialist Projects, Paper 1484, 2015 (A002415, A000332, A006542, A006857, A108679)
  354. 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.
  355. Wayne Barrett, Shaun Fallat, Veronika Furst, Shahla Nasserasr, Brendan Rooney, and Michael Tait, Regular Graphs of Degree at most Four that Allow Two Distinct Eigenvalues, arXiv:2305.10562 [math.CO], 2023. (A006820)
  356. Christian Barrientos, Sarah Minion, Enumerating Families of Labeled Graphs, Journal of Integer Sequences, 18 (2015), # 15.1.7.
  357. 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
  358. Christian Barrientos, Sarah Minion, On the number of α-labeled graphs, Discussiones Mathematicae Graph Theory, to appear, doi:10.7151/dmgt.1985
  359. Christian Barrientos, Sarah Minion, Series-Parallel Operations with Alpha-Graphs, Theory and Applications of Graphs (2019) Vol. 6, Issue 1, Article 4. Abstract (A032121)
  360. Michael D. Barrus, Weakly threshold graphs, arXiv preprint arXiv:1608.01358, 2016
  361. M. D. Barrus, S. G. Hartke, Minimal forbidden sets for degree sequence characterizations, 2013; PDF Discr. Math 338 (9) (2015) 1543 doi:10.1016/j.disc.2015.02.018
  362. Paul Barry, "A Catalan Transform and Related Transformations on Integer Sequences", J. Integer Sequences, Volume 8, 2005, Article 05.4.5.
  363. Paul Barry, "On Integer-Sequence-Based Constructions of Generalized Pascal Triangles", J. Integer Sequences, Volume 9, 2006, Article 06.2.4.
  364. Paul Barry, "On a Family of Generalized Pascal Triangles Defined by Exponential Riordan Arrays", J. Integer Sequences, Volume 10, 2007, Article 07.3.5.
  365. Paul Barry, "Some Observations on the Lah and Laguerre Transforms of Integer Sequences", J. Integer Sequences, Volume 10, 2007, Article 07.4.6.
  366. Paul Barry, On Integer Sequences Associated With the Cyclic and Complete Graphs, J. Integer Sequences, Volume 10, 2007, Article 07.4.8.
  367. Paul Barry, A Note on Krawtchouk Polynomials and Riordan Arrays, JIS 11 (2008) 08.2.2
  368. 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).
  369. P. Barry, A Note on a One-Parameter Family of Catalan-Like Numbers, JIS 12 (2009) 09.5.4
  370. P. Barry, Continued fractions and transformations of integer sequences, JIS 12 (2009) 09.7.6
  371. P. Barry, Symmetric Third-Order Recurring Sequences, Chebyshev Polynomials, and Riordan Arrays, JIS 12 (2009) 09.8.6
  372. P. Barry, Generalized Catalan Numbers, Hankel Transforms and Somos-4 Sequences, J. Int. Seq. 13 (2010) #10.7.2.
  373. P. Barry, The Restricted Toda Chain, Exponential Riordan Arrays, and Hankel Transforms, J. Int. Seq. 13 (2010) # 10.8.4
  374. P. Barry, Exponential Riordan Arrays and Permutation Enumeration, J. Int. Seq. 13 (2010) # 10.9.1
  375. Barry, Paul, Riordan arrays, orthogonal polynomials as moments, and Hankel transforms. J. Integer Seq. 14 (2011), no. 2, Article 11.2.2, 37 pp.
  376. Barry, Paul, On the central coefficients of Bell matrices. J. Integer Seq. 14 (2011), no. 4, Article 11.4.3, 10 pp.
  377. Barry, Paul, On a generalization of the Narayana triangle. J. Integer Seq. 14 (2011), no. 4, Article 11.4.5, 22 pp.
  378. Paul Barry, Eulerian polynomials as moments, via exponential Riordan arrays, Arxiv preprint arXiv:1105.3043, 2011, and JIS 14 (2011) # 11.9.5
  379. 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.
  380. P. Barry, Invariant number triangles, eigentriangles and Somos-4 sequences, Arxiv preprint arXiv:1107.5490, 2011.
  381. P. Barry, On sequences with {-1, 0, 1} Hankel transforms, Arxiv preprint arXiv:1205.2565, 2012
  382. 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.
  383. P. Barry, Riordan-Bernstein Polynomials, Hankel Transforms and Somos Sequences, Journal of Integer Sequences, Vol. 15 2012, #12.8.2.
  384. Paul Barry, On the Hurwitz Transform of Sequences, Journal of Integer Sequences, Vol. 15 (2012), #12.8.7.
  385. P. Barry, On the Hankel transform of C-fractions, arXiv preprint arXiv:1212.3490, 2012
  386. P. Barry, On the Central Coefficients of Riordan Matrices, Journal of Integer Sequences, 16 (2013), #13.5.1.
  387. P. Barry, A Note on a Family of Generalized Pascal Matrices Defined by Riordan Arrays, Journal of Integer Sequences, 16 (2013), #13.5.4.
  388. 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.
  389. 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.
  390. Paul Barry, Laurent Biorthogonal Polynomials and Riordan Arrays, arXiv preprint arXiv:1311.2292, 2013
  391. P. Barry, General Eulerian Polynomials as Moments Using Exponential Riordan Arrays, Journal of Integer Sequences, 16 (2013), #13.9.6.
  392. P. Barry, Embedding structures associated with Riordan arrays and moment matrices, arXiv preprint arXiv:1312.0583, 2013
  393. 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
  394. P. Barry, Generalized Stirling Numbers, Exponential Riordan Arrays, and Toda Chain Equations, Journal of Integer Sequences, 17 (2014), #14.2.3.
  395. P. Barry, Constructing Exponential Riordan Arrays from Their A and Z Sequences, Journal of Integer Sequences, 17 (2014), #14.2.6.
  396. P Barry, Riordan arrays, generalized Narayana triangles, and series reversion, Linear Algebra and its Applications, 491 (2016) 343–385.
  397. Paul Barry, Riordan Arrays: A Primer, Logic Press, 2016.
  398. Paul Barry, Jacobsthal Decompositions of Pascal's Triangle, Ternary Trees, and Alternating Sign Matrices, - Journal of Integer Sequences, 19, 2016, #16.3.5.
  399. Paul Barry, On the Group of Almost-Riordan Arrays, arXiv preprint arXiv:1606.05077, 2016
  400. Paul Barry, Eulerian-Dowling Polynomials as Moments, Using Riordan Arrays, arXiv:1702.04007 [math.CO], 2017.
  401. Paul Barry, A Note on d-Hankel Transforms, Continued Fractions, and Riordan Arrays, arXiv:1702.04011 [math.CO], 2017.
  402. Paul Barry, Sigmoid functions and exponential Riordan arrays, arXiv:1702.04778 [math.CA], 2017.
  403. Paul Barry, Power series, the Riordan group and Hopf algebras, arXiv:1706.01323 [math.CO], 2017.
  404. 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)
  405. 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."
  406. 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)
  407. 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)
  408. 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)
  409. 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)
  410. 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)
  411. 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)
  412. Paul Barry, On the halves of a Riordan array and their antecedents, arXiv:1906.06373 [math.CO], 2019. (A007318, A264772)
  413. Paul Barry, On the r-shifted central triangles of a Riordan array, arXiv:1906.01328 [math.CO], 2019. (A007318)
  414. 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)
  415. 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)
  416. 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)
  417. 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)
  418. 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)
  419. 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)
  420. 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)
  421. Paul Barry, Notes on the Hankel transform of linear combinations of consecutive pairs of Catalan numbers, arXiv:2011.10827 [math.CO], 2020. (A000108, A001519, A001906, A007318, A039598, A039599, A078812, A078920, A085478, A123352, A197649)
  422. Paul Barry, The second production matrix of a Riordan array, arXiv:2011.13985 [math.CO], 2020. (A000108, A007318, A033184, A085478, A092276)
  423. Paul Barry, On the inversion of Riordan arrays, arXiv:2101.06713 [math.CO], 2021. (A000108, A001263, A001662, A002002, A007318, A009766, A049310, A053121, A060693, A084938, A088617, A094587, A097610, A119467, A126216, A196347, A243662, A243663, A249925)
  424. Paul Barry, On the duals of the Fibonacci and Catalan-Fibonacci polynomials and Motzkin paths, arXiv:2101.10218 [math.CO], 2021. (A000045, A011973, A097610, A098614, A107131, A109187, A111959, A200375)
  425. Paul Barry, Centered polygon numbers, heptagons and nonagons, and the Robbins numbers, arXiv:2104.01644 [math.CO], 2021. (A000045, A000108, A000124, A000217, A000975, A001045, A001764, A001844, A002061, A002478, A005021, A005130, A005156, A005157, A005329, A005448, A005809, A005891, A006013, A007226, A007318, A007440, A030981, A047098, A047099, A047749, A049126, A049130, A052536, A052547, A052941, A052975, A072405, A077954, A077998, A080937, A080956, A088927, A094706, A094832, A094833, A098746, A099325, A104769, A106509, A115140, A120981, A120984, A121449, A121545, A122100, A122368, A127896, A127897, A130713, A134565, A154272, A186185, A188022, A188687, A200715, A215404, A305573, A321511, A339850)
  426. Paul Barry, On the Gap-sum and Gap-product Sequences of Integer Sequences, arXiv:2104.05593 [math.CO], 2021. (A000045, A000012, A000040, A000108, A000129, A001045, A001710, A001764, A002293, A002294, A002295, A002605, A005585, A014707, A006002, A048395, A054265, A088748, A102693, A103897, A109454)
  427. Paul Barry, Conjectures and results on some generalized Rueppel sequences, arXiv:2107.00442 [math.CO], 2021. (A000108, A000957, A005811, A006257, A014577, A036563, A036987, A037834, A043545, A043725, A062050, A088567, A088748, A110036, A126983, A268411, A339422)
  428. Paul Barry, Series reversion with Jacobi and Thron continued fractions, arXiv:2107.14278 [math.NT], 2021. (A000045, A000108, A000142, A000522, A000629, A000670, A000828, A000957, A001003, A001045, A003543, A005439, A033321, A046802, A049774, A080635, A092107, A110501, A114710, A133314, A152163, A162975, A234797)
  429. Paul Barry, Conjectures on Somos 4, 6 and 8 sequences using Riordan arrays and the Catalan numbers, arXiv:2211.12637 [math.CO], 2022. (A000108, A004148, A135052)
  430. Paul Barry, On Motzkin-Schröder Paths, Riordan Arrays, and Somos-4 Sequences, J. Int. Seq. (2023) Vol. 26, Art. 23.4.7. HTML (A000012, A000045, A000108, A001006, A006318, A025235, A059317, A059345, A059398, A059841, A060693, A064189, A071359, A078481, A084782, A085139, A102407, A103210, A128720, A132276, A132277, A143013, A174168, A184019, A190156, A190252, A247333)
  431. Paul Barry, Integer sequences from elliptic curves, arXiv:2306.05025 [math.NT], 2023. (A000045, A000108, A000129, A006720, A006769, A025262, A056010, A157003, A178072, A178078, A178079)
  432. Paul Barry, Moment sequences, transformations, and Spidernet graphs, arXiv:2307.00098 [math.CO], 2023. (A000108, A000957, A000958, A001003, A001006, A001519, A001850, A002426, A005043, A064189, A109190, A111961)
  433. 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.
  434. P. Barry, A. Hennessey, Notes on a Family of Riordan Arrays and Associated Integer Hankel Transforms, JIS 12 (2009) 09.5.3
  435. P. Barry, A. Hennessy, The Euler-Seidel Matrix, Hankel Matrices and Moment Sequences, J. Int. Seq. 13 (2010) # 10.8.2
  436. P. Barry, A. Hennessy, Meixner-Type Results for Riordan Arrays and Associated Integer Sequences, J. Int. Seq. 13 (2010) # 10.9.4
  437. P. Barry and A. Hennessy, Four-term Recurrences, Orthogonal Polynomials and Riordan Arrays, Journal of Integer Sequences, 2012, article 12.4.2.
  438. 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.
  439. 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.
  440. Paul Barry and Aoife Hennessy, Generalized Narayana Polynomials, Riordan Arrays, and Lattice Paths, Journal of Integer Sequences, Vol. 15, 2012, #12.4.8.
  441. Paul Barry, Aoife Hennessy, Nikolaos Pantelidis, Algebraic properties of Riordan subgroups, ResearchGate preprint (2020). Abstract (A000012, A000045, A000108, A004148)
  442. 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)
  443. D. Barsky, J.-P. Bézivin, p-adic Properties of Lengyel's Numbers, Journal of Integer Sequences, 17 (2014), #14.7.3.
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  445. Simon Barthelmé, Konstantin Usevich, Spectral properties of kernel matrices in the flat limit, arXiv:1910.14067 [math.NA], 2019. Orderings page
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