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"Steven R. Finch's incredible labor of love, an encyclopedia of mathematical constants, begins with such basics, then moves on to more elaborate topics. ... It appears astonishing to me that a single individual went through all these topics. His achievement can only be compared to the On-Line Encyclopedia of Integer Sequences." [Osmo Pekonen, 2019]

"As a researcher in combinatorics, one of my favorite tools is the On-Line Encyclopedia of Integer Sequences, or OEIS. This database was started by the mathematician Neil Sloane, who first started keeping an index of popular sequences of integers that came up in his work. At the time, Sloane was a graduate student at Cornell University. A photo of the first page of Sloane’s notebook is shown in Figure 7.1. Recognize any of these sequences?" [T. Kyle Petersen, 2019]

"... we'd like to thank to OEIS editors Michel Marcus, Peter Luschny, Jon E. Schoenfield and others for their patient, faithful volunteer work and for useful comments and suggestions during the editing of sequences, concerned with this manuscript." [Kolosov Petro. 2019]

"On p. 18, notes that the OEIS was used to find relevant literature." [Robert A. Proctor and Matthew J. Willis, 2017]

"All three authors would like to acknowledge the On-Line Encyclopedia of Integer Sequences [Slo14], without which this project would have been very difficult." [Nicholas Proudfoot, Max Wakefield, and Ben Young, 2015]

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  • This section lists works in which the first author's name begins with P.
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References

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  2. Arun Padakandla, P.R. Kumar, Wojciech Szpankowski, Preserving Privacy and Fidelity via Ehrhart Theory, July 2017.
  3. R. Padmanabhan, Alok Shukla, Orchards in elliptic curves over finite fields, arXiv:2003.07172 [math.NT], 2020. (A003035)
  4. Martin Paech, Numerische und algebraisch-graphentheoretische Algorithmen für korrelierte Quantensysteme, Dissertation, Hannover: Fakultät für Mathematik und Physik der Leibniz Universität, 2015.
  5. M. Paech, W. Apel, E. Kalinowski and E. Jeckelmann, Comparison of computer-algebra strong-coupling perturbation theory and dynamical mean-field theory for the Mott-Hubbard insulator in high dimensions, Phys. Rev. B 90 (24), 245147 (2014), 10 pages, doi:10.1103/PhysRevB.90.245147. Also arXiv:1410.6630, 2014.
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  17. Jean-Christophe Pain, An exact series expansion for the Dottie number, arXiv:2303.17962 [math.NT], 2023. (A182503)
  18. Jean-Christophe Pain, Series representations for the logarithm of the Glaisher-Kinkelin constant, arXiv:2304.07629 [math.NT], 2023. (A002109, A143475, A143476)
  19. Jean-Christophe Pain, Bounds on the p-adic valuation of the factorial, hyperfactorial and superfactorial, arXiv:2408.00353 [math.NT], 2024. (A002109, A046882)
  20. Jean-Christophe Pain and Brian G. Wilson, Fast approximation to supershell partition functions: Explicit forms of the coefficients, High Energy Density Phys. (2023) 101065. doi:10.1016/j.hedp.2023.101065
  21. Jesse Pajwani, Herman Rohrbach, and Anna M. Viergever, Compactly supported ℀¹-Euler characteristics of symmetric powers of cellular varieties, arXiv:2404.08486 [math.AG], 2024. See p. 15. (A034851)
  22. I. Pak, Partition Identities and Geometric Bijections, Proc. Amer. Math. Soc. 132 (2004), 3457-3462.
  23. Igor Pak, History of Catalan numbers, arXiv:1408.5711, 2014.
  24. Igor Pak, Complexity problems in enumerative combinatorics, arXiv:1803.06636 [math.CO], 2018. (A000055, A000081, A000110, A000123, A000607, A000929, A001156, A002829, A003107, A005130, A006318, A007279, A007294, A033552, A064986, A076478, A082640, A151353, A250102)
  25. Diyath Pannipitiya, To Symbolic Dynamics Through The Thue-Morse Sequence, arXiv:2402.07015 [math.DS], 2024. (A000044 p. 1, A010060 pp. 1, 14)
  26. I. Pak and G. Panova, Unimodality via Kronecker products, arXiv preprint arXiv:1304.5044, 2013.
  27. Igor Pak, Greta Panova, Bounds on Kronecker coefficients via contingency tables, Linear Algebra and its Applications (2020), Vol. 602, 157-178. doi:10.1016/j.laa.2020.05.005, also PDF (A000700, A059867)
  28. I. Pak, G. Panova, E. Vallejo, Kronecker products, characters, partitions, and the tensor square conjectures, arXiv:1304.0738, 2013
  29. Igor Pak, Greta Panova, Damir Yeliussizov, On the largest Kronecker and Littlewood-Richardson coefficients, arXiv:1804.04693 [math.CO], 2018. (A003040, A070933, A110143)
  30. I. Pak, A. Soffer, On Higman's k(U_n(F_q)) conjecture, arXiv preprint arXiv:1507.00411, 2015.
  31. Apisit Pakapongpun, Thomas Ward, Functorial orbit counting (2009) arXiv:0901.2646 and JIS 12 (2009) 09.2.4
  32. F. Pakovich, A. K. Zvonkin, Minimum degree of the difference of two polynomials over Q, and weighted plane trees, Selecta Mathematica, New Ser. 2014; doi:10.1007/s00029-014-0151-0
  33. M. B. Paksoy, Derived Ramanujan Primes: R'_{N}, arXiv preprint arXiv:1210.6991, 2012.
  34. J. A. Palacios, A. Bhaskar, F. Disanto and N. A. Rosenberg, Enumeration of binary trees compatible with a perfect phylogeny, J. Math. Biol. 84 (2022), 54. doi:10.1007/s00285-022-01748-w (A065619, A162171)
  35. S. Palasek, Non-Cooperativity in Bayesian Social Learning, arXiv preprint arXiv:1407.0519, 2014.
  36. Sushma Palimar and B. R. Shankar, Mersenne Primes in Real Quadratic Fields, Journal of Integer Sequences, Vol. 15 (2012), #12.5.6.
  37. J. M. Pallo, On the listing and random generation of hybrid binary trees, International Journal of Computer Mathematics, 50, 1994, 135-145.
  38. Jean Pallo, doi:10.1016/S0020-0190(00)00008-9 An efficient upper bound of the rotation distance of binary trees, Information Processing Letters, Volume 73, Issues 3-4, 29 February 2000, Pages 87-92.
  39. Jean Marcel Pallo, Weak associativity and restricted rotation, Information Processing Letters, Volume 109, Issue 10, 30 April 2009, Pages 514-517.
  40. M. Palmacci, Escher's Problem and Numerical Sequences, (2006)
  41. M. G. Palomo, Latin polytopes, arXiv preprint arXiv:1402.0772, 2014.
  42. Rogério Paludo and Leonel Sousa, Number Theoretic Transform Architecture suitable to Lattice-based Fully-Homomorphic Encryption, 2021 IEEE 32nd Int'l Conf. Appl.-specific Sys., Architectures and Processors (ASAP) 163-170. doi:10.1109/ASAP52443.2021.00031 (A080076)
  43. Hao Pan, Z.-W. Sun, Consecutive primes and Legendre symbols, arXiv preprint arXiv:1406.5951, 2014.
  44. Hao Pan and Zhi-Wei Sun, Supercongruences for central trinomial coefficients, arXiv:2012.05121 [math.NT], 2020. (A002426, A208425, A277640)
  45. J. Pan, Multiple Binomial Transforms and Families of Integer Sequences, J. Int. Seq. 13 (2010), 10.4.2.
  46. Pan, Jiaqiang Some properties of the multiple binomial transform and the Hankel transform of shifted sequences. J. Integer Seq. 14 (2011), no. 3, Article 11.3.4, 8 pp.
  47. J. Pan, Matrix Decomposition of the Unified Generalized Stirling Numbers and Inversion of the Generalized Factorial Matrices, Journal of Integer Sequences, 15 (2012) #12.6.6.
  48. J. Pan, Convolution Properties of the Generalized Stirling Numbers and the Jacobi-Stirling Numbers of the First Kind, Journal of Integer Sequences, 16 (2013), #13.9.2.
  49. Qiong Qiong Pan, Jiang Zeng, The γ-coefficients of Branden's (p,q)-Eulerian polynomials and André permutations, arXiv:1910.01747 [math.CO], 2019. (A000111, A122852)
  50. Qiongqiong Pan and Jiang Zeng, Cycles of even-odd drop permutations and continued fractions of Genocchi numbers, arXiv:2108.03200 [math.CO], 2021. (A005439)
  51. Ran Pan, Block patterns in permutations and words and generalized clusters, Ph. D. Dissertation, Univ. Calif. San Diego, 2016.
  52. Ran Pan, Dun Qiu, Jeffrey Remmel, Counting Consecutive Pattern Matches in S_n(132) and S_n(123), arXiv:1809.01384 [math.CO], 2018. Also in Advances in Applied Mathematics (2019) Vol. 105, 130-167. doi:10.1016/j.aam.2019.01.005 (A001006)
  53. R. Pan, J. B. Remmel, Paired patterns in lattice paths, arXiv:1601.07988 (2016)
  54. Pan, Shu-Wen. & Pan, JQ., Direct solutions of linear non-homogeneous difference equations, Adv Differ Equ (2016) 2016: 108. doi:10.1186/s13662-016-0839-x
  55. Zan Pan, Conjectures on the number of Langford sequences, (2021). PDF (A014552, A059106, A125762)
  56. D. Panario, M. Sahin, Q. Wang, A family of Fibonacci-like conditional sequences, INTEGERS, Vol. 13, 2013, #A78.
  57. D. Panario, M. Sahin, Q. Wang, W. Webb, General conditional recurrences, Applied Mathematics and Computation, Volume 243, 15 September 2014, Pages 220-231.
  58. A Panayotopoulos, On Meandric Colliers, Mathematics in Computer Science, (2018). https://doi.org/10.1007/s11786-018-0389-6.
  59. A. Panayotopoulos and P. Tsikouras, "Meanders and Motzkin Words", J. Integer Sequences, Volume 7, 2004, Article 04.1.2.
  60. A. Panayotopoulos and P. Vlamos, Cutting Degree of Meanders, Artificial Intelligence Applications and Innovations, IFIP Advances in Information and Communication Technology, Volume 382, 2012, pp 480-489;doi:10.1007/978-3-642-33412-2_49.
  61. A. Panayotopoulos, P. Vlamos, Partitioning the Meandering Curves, Mathematics in Computer Science (2015) p 1-10, doi:10.1007/s11786-015-0234-0. (A000136, A005316, A000682, A000560, A217310, A217318, A227167)
  62. Kanupriya Pande, Jeffrey J. Donatelli, et al., Free-electron laser data for multiple-particle fluctuation scattering analysis, Scientific Data volume 5, Article number: 180201 (2018). doi:10.1038/sdata.2018.201
  63. Ashish Kumar Pandey and B. K. Sharma, On Inequalities Related to a Generalized Euler Totient Function and Lucas Sequences, J. Int. Seq. (2023) Vol. 26, Art. 23.8.6. Abstract (A000045, A000129, A001109)
  64. Ashish Kumar Pandey and Brajesh Kumar Sharma, A Note On Magic Squares And Magic Constants, Appl. Math. E-Notes (2023) Vol. 23, Art. No. 53, 577-582. PDF (A006003 p. 577)
  65. Ram Krishna Pandey, "On Some Magnified Fibonacci Numbers Modulo a Lucas Number" , Journal of Integer Sequences, Vol. 16 (2013), #13.1.7.
  66. Rohan Pandey and Harry Richman, The Möbius function of the poset of triangular numbers under divisibility, arXiv:2402.07934 [math.NT], 2024. (A350682, A351167) (A350682 pp. 2, 7, A351167 pp. 2, 8)
  67. V. Pandichelvi, P. Sivakamasundari, M. A. Gopalan, On the Negative Pell Equation y^2 = 54 x^2 - 5, International Journal of Mathematics Trends and Technology- Volume 21 Number 1, pages 16-20.
  68. Sabrina X. M. Pang and Lun Lv, A Refinement of Leaves on Noncrossing Trees, Graphs and Combinatorics, 2011, doi:10.1007/s00373-011-1097-z.
  69. Alois Panholzer, Parking function varieties for combinatorial tree models, arXiv:2007.14676 [math.CO], 2020. (A000139, A006318, A010050, A214377, A294084)
  70. Alois Panholzer, Consecutive permutation patterns in trees and mappings, J. of Combinatorics, (2021) Vol. 12, No. 1. doi:10.4310/JOC.2021.v12.n1.a2
  71. Alexei Pantchichkine, Constructions of p-adic L-functions and admissible measures for Hermitian modular forms, Number Theory [math.NT], 2018. Abstract (A047817)
  72. Alexei Pantchichkine, Algebraic differential operators on arithmetic automorphic forms, modular distributions, p-adic interpolation of their critical l values via BGG modules and Hecke algebras, J. Math. Math. Sci., Thang Long Univ. (Viet Nam, 2022) Vol. 1, No. 4, 1-26. PDF (A047817)
  73. Jay Pantone, The Enumeration of Permutations Avoiding 3124 and 4312, arXiv preprint arXiv:1309.0832, 2013.
  74. Jay Pantone, The enumeration of inversion sequences avoiding the patterns 201 and 210, arXiv:2310.19632 [math.CO], 2023. (A212198, A263778 p. 12, A263780 p. 12, A279555 p. 14, A000079, A000110, A001519, A006318, A200753, A263777, A263778, A263779, A263780)
  75. N. Panyunin, Messner's theorem, Kvant, 2022, 9, 11–15. [in Russian]
  76. D. Panyushev, On the orbits of a Borel subgroup in abelian ideals, arXiv preprint arXiv:1407.6857, 2014
  77. G. Paoletti, Deterministic Abelian Sandpile Models and Patterns, Ph. D. Thesis, Universita di Pisa, Scuola di dottorato Scienze di base "Galileo Galilei", Pisa, 2013; PDF.
  78. L. A. Papakonstantinidis, The win-win-win papakonstantinidis model: The limit of the Sensitization Process (2019). doi:10.13140/RG.2.2.16575.15529 (A002162, A002391, A002392, A007524, A016627, A016628, A016629, A016630, A016631, A016632, A020862)
  79. Dimitris Papamichail, Angela Huang, Edward Kennedy, Jan-Lucas Ott, Andrew Miller, Georgios Papamichail, Live phylogeny with polytomies: Finding the most compact parsimonious trees, Computational Biology and Chemistry, Volume 69, August 2017, p. 171-177. doi:10.1016/j.compbiolchem.2017.03.013, arXiv preprint arXiv:1603.03315 [cs.DS], 2016.
  80. G. Paquin, Dénombrement de multigraphes enrichis, Mémoire, Math. Dept., Univ. Québec à Montréal, 2004.
  81. Daniel Pareja, Prime Number Races, PDF
  82. Param Parekh, Paavan Parekh, Sourav Deb, and Manish K. Gupta, On the Classification of Weierstrass Elliptic Curves over ℤn, arXiv:2310.11768 [cs.CR], 2023. (A000224, A046530, A238533)
  83. Matteo Parisi, Melissa Sherman-Bennett, Ran Tessler, and Lauren Williams, The Magic Number Conjecture for the m=2 amplituhedron and Parke-Taylor identities, arXiv:2404.03026 [math.CO], 2024. See p. 8. (A175124)
  84. Matteo Parisi, Melissa Sherman-Bennett, and Lauren Williams, The m=2 amplituhedron and the hypersimplex: signs, clusters, triangulations, Eulerian numbers, arXiv:2104.08254 [math.CO], 2021. (A175124)
  85. D. Parisse, The Tower of Hanoi and the Stern-Brocot Array, Thesis, Ludwig-Maximilians-Universitaet Munich, August 1997.
  86. Daniele Parisse, On hypersequences of an arbitrary sequence and their weighted sums, Integers (2024) Vol. 24, Art. No. A70. PDF (A000012, A000032, A000045, A000557, A063524, A263968)
  87. Boram Park and Seonjeong Park, Shellable posets arising from even subgraphs of a graph, arXiv:1705.06423 [math.CO], 2017.
  88. Donghwi Park, Space-state complexity of Korean chess and Chinese chess, arXiv preprint arXiv:1507.06401, 2015.
  89. GaYee Park, Naruse hook formula for linear extensions of mobile posets, arXiv:2104.11166 [math.CO], 2021. (A332471, A332568)
  90. Gunwoong Park, High-Dimensional Poisson DAG Model Learning Using l_1-Regularized Regression, arXiv:1810.02501 [stat.ML], 2018.
  91. Ki-Hyeon Park and Hong-Yeop Song, Some Properties of Binary Matrices and Quasi-Orthogonal Signals Based on Hadamard Equivalence, IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences Vol.E95-A No.11 pp.1862-1872, 2012.
  92. Poo-Sung Park, Multiplicative functions with f(p + q − n0) = f(p) + f(q) − f(n0), arXiv:2002.09908 [math.NT], 2020. (A057778, A126717)
  93. Sang-Hoon Park, Abdelmejid Bayad, Daeyeoul Kim, Divisor functions and Polygon Shape Numbers, Draft of Proceedings Book of the 2nd Mediterranean International Conference of Pure & Applied Mathematics and Related Areas (MICOPAM 2019), 1-3. PDF
  94. Seonjeong Park, Real toric manifolds and shellable posets arising from graphs, 2018. PDF (A071721)
  95. So Ryoung Park, Jinsoo Bae, Hyun Gu Kang, Iickho Song, doi:10.1090/S0025-5718-07-02082-0 On the polynomial representation for the number of partitions with fixed lengths, Math. Comp. vol. 77, no. 262 (2008) 1135-1151.
  96. Y. Park, S. Park, Avoiding permutations and the Narayana numbers, J. Korean Math. Soc. 50 (2013), No. 3, pp. 529-541, doi:10.4134/JKMS.2013.50.3.529
  97. Park, Youngja, and SeungKyung Park. "Enumeration of generalized lattice paths by string types, peaks, and ascents." Discrete Mathematics 339.11 (2016): 2652-2659.
  98. Daniel E. Parker, Romain Vasseur, Joel E. Moore, Entanglement Entropy in Excited States of the Quantum Lifshitz Model, arXiv:1702.07433 [cond-mat.stat-mech], 2017.
  99. Douglas Stott Parker and Prasad Ram, The construction of Huffman codes is a submodular ("convex") optimization problem over a lattice of binary trees. SIAM J. Comput. 28 (1999), no. 5, 1875-1905 (electronic).
  100. M. G. Parker, Conjectures on the Size of Constellations Constructed from Direct Sums of PSK Kernels, LNCS 1719, Presented in part at 13th International Symposium, AAECC-13, Honolulu, Hawaii, pp 420-429, 14-19 Nov, 1999. (postscript, PDF)
  101. M. G. Parker, Spectrally Bounded Sequences, Codes and States: Graph Constructions and Entanglement, Invited Talk at Eighth IMA International Conference on Cryptography and Coding, Cirencester, UK, 17-19 December, 2001, LNCS 2260, pp. 339ff. (2001). (PostScript, Pdf)
  102. M. G. Parker and C. Tellambura, A Construction for Binary Sequence Sets with Low Peak-to-Average Power Ratio, Reports in Informatics, University of Bergen, Report No 242, ISSN 0333-3590, February 2003. (PostScript, PDF)
  103. Matt Parker, <a href="https://www.youtube.com/watch?v=ErBbyLu-M94">The mystery of 0.866025403784438646763723170752936183471402626905190314027903489</a>, Stand-up Maths, Youtube video, Feb 14 2024 (A010527)
  104. J. Parkkonen and F. Paulin, doi:10.2140/gt.2010.14.277, Prescribing the behaviour of geodesics in negative curvature, Geom. Topol. 14 (2010) 277-392.
  105. James M. Parks, Computing Pythagorean Triples, arXiv:2107.06891 [math.GM], 2021. (A001653, A096033)
  106. James M. Parks, On the Curved Patterns Seen in the Graph of PPTs, arXiv:2104.09449 [math.CO], 2021. (A096033)
  107. Bernhard R. Parodi, A generalized Fibonacci spiral, arXiv:2004.08902 [math.HO], 2020.
  108. A. Parreau, M. Rigo, E. Rowland, and E. Vandomme, A new approach to the 2-regularity of the l-abelian complexity of 2-automatic sequences, arXiv preprint arXiv:1405.3532, 2014.
  109. S. Parthasarathy, Special characters in LATEX, (2021). PDF
  110. Robert Parviainen, "Lattice Path Enumeration of Permutations with k Occurrences of the Pattern 2-13", J. Integer Sequences, Volume 9, 2006, Article 06.3.2.
  111. Robert Parviainen, "Parametric Production Matrices and Weighted Succession Rules: a Dyck Path Example", J. Integer Sequences, Volume 10, 2007, Article 07.6.1.
  112. Robert Parviainen, Some bijections on set partitions (2007), arXiv:0710.1132.
  113. J. Pasukonis, S. Ramgoolam, From counting to construction for BPS states in N=4SYM, J. High En. Phys. 2011 (2) (2011) # 078 arXiv:1010.1683 doi:10.1007/JHEP02(2011)078
  114. Ludovic Patey, Ramsey-like theorems and moduli of computation, arXiv:1901.04388 [math.LO], 2019. (A000108)
  115. A. Pathak, Non-Hermitian quantum gates are more common than Hermitian quantum gates, arXiv preprint arXiv:1309.4037, 2013.
  116. Pathak, Aritro. "On certain partition bijections related to Euler's partition problem." Discrete Mathematics 345.2 (2022): 112673.
  117. Anuj Pathania, Scalable Task Schedulers for Many-Core Architectures, Ph.D. Thesis, Karlsruher Instituts für Technologie (Germany, 2018). doi:10.5445/IR/1000082991 (A000105)
  118. Anuj Pathania, Vanchinathan Venkataramani, Muhammad Shafique, Tulika Mitra, Jörg Henkel, Defragmentation of Tasks in Many-Core Architecture, ACM Transactions on Architecture and Code Optimization (TACO), Volume 14 Issue 1, April 2017, Article No. 2. doi:10.1145/3050437
  119. G. K. Patil, Ramanujan's Life And His Contributions In The Field Of Mathematics, International Journal of Scientific Research and Engineering Studies (IJSRES), Volume 1 Issue 6, December 2014, ISSN: 2349-8862; http://www.ijsres.com/2014/vol-1_issue-6/paper_8.pdf
  120. N. Patson, Pisano period and permutations of n X n matrices, Australian Math. Soc. Gazette, 2007.
  121. Elena Patyukova, Taylor Rottreau, Robert Evans, Paul D. Topham, Martin J. Greenall, Hydrogen bonding in acrylamide and its role in the scattering behavior of acrylamide-based block copolymers. arXiv:1805.09878 [cond-mat.soft], 2018. Also in Macromolecules (2018) Vol. 51, No. 18, 7032-7043. doi:10.1021/acs.macromol.8b01118 (A000108, A000309)
  122. Elena Patyukova, Taylor Rottreau, Robert Evans, Paul D. Topham, Martin J. Greenall, Supporting information: Hydrogen bonding aggregation in acrylamide: theory and experiment, Aston University (Birmingham, England 2019), S12. PDF (A000309)
  123. Paukner, M., Pepin, L., Riehl, M., and Wieser, J., Pattern Avoidance in Task-Precedence Posets, arXiv:1511.00080
  124. Neeraj Kumar Paul and Helen K. Saikia, A generalization of Fibonacci sequence, Proyecciones (Chile 2020) Vol. 39, 1393-1405. doi:10.22199/issn.0717-6279-2020-06-0085 (A000045)
  125. Neeraj Kumar Paul and Helen K. Saikia, Some generalized results related to Fibonacci sequence, Proyecciones (Chile 2021) Vol. 40, No. 3, 605-617. doi:10.22199/issn.0717-6279-4269 (A000045)
  126. Shubhankar Paul, Ten Problems of Number Theory, International Journal of Engineering and Technical Research (IJETR), ISSN: 2321-0869, Volume-1, Issue-9, November 2013
  127. Shubhankar Paul, Legendre, Grimm, Balanced Prime, Prime triplet, Polignac's conjecture, a problem and 17 tips with proof to solve problems on number theory, International Journal of Engineering and Technical Research (IJETR), ISSN: 2321-0869, Volume-1, Issue-10, December 2013; http://erpublication.org/admin/vol_issue1/upload%20Image/IJETR012013.pdf
  128. W. Paulsen, Calkin-Wilf sequences for irrational numbers, Fib. Q., 61:1 (2023), 51-59.
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  407. Helmut Prodinger, S-Motzkin paths with catastrophes and air pockets, arXiv:2302.07233 [math.CO], 2023.
  408. Helmut Prodinger, Grand Motzkin paths and {0,1,2}-trees — a simple bijection, arXiv:2308.07884 [math.CO], 2023. (A001006) In the encyclopedia [9] they are enumerated by sequence A001006, with many references given. [9] Neil J. A. Sloane and The OEIS Foundation Inc. The On-Line Encyclopedia of Integer Sequences, 2023.
  409. Helmut Prodinger, Motzkin paths of bounded height with two forbidden contiguous subwords of length two, arXiv:2310.12497 [math.CO], 2023. (A004149, A023431, A217282, A308435, A329666, A329676, A329701, A329702)
  410. Helmut Prodinger, Prefixes of Stanley's Catalan paths with odd returns to the x-axis — standard version and skew Catalan-Stanley paths, arXiv:2402.01429 [math.CO], 2024. (A002212)
  411. Helmut Prodinger, Partial Dyck path interpretation for three sequences in the Encyclopedia of Integer Sequences, arXiv:2408.01290 [math.CO], 2024. (A101785, A113337, A143017)
  412. Helmut Prodinger and Sarah J. Selkirk, Sums of squares of Tetranacci numbers: A generating function approach, arXiv:1906.08336 [math.NT], 2019. (A000078)
  413. H. Prodinger and T. A. Tshifhumulo, On q-Olivier functions, Annals of Combinatorics, 6 (2002), no. 2, 181-194.
  414. J. Propp, Integrability, Exact Solvability and Algebraic Combinatorics: A Three-Way Bridge?, presented in the Workshop on Combinatorics and Integrable Models, Canberra, 2002.
  415. J. Propp, Tilings, Chapter 9 in Miklos Bona, editor, Handbook of Enumerative Combinatorics, CRC Press, 2015, pages 541-588.
  416. J. Propp, Lessons I learned from Richard Stanley, arXiv preprint arXiv:1501.00719, 2015.
  417. James Propp, Some 2-Adic Conjectures Concerning Polyomino Tilings of Aztec Diamonds, Integers (2023) Vol. 23, Art. A30. doi:10.5281/zenodo.7859005, PDF (A004003, A065072, A071093, A356512, A356513, A356514, A356523) See also <a href="https://doi.org/10.5281/zenodo.7859005">Integers</a> (2023) Vol. 23, Art. A30.
  418. J. Propp and D. Ullman, On the Cookie Game, International Journal of Game Theory, volume 20 (1992), pages 313-324.
  419. Nicholas Proudfoot, Max Wakefield, and Ben Young, Intersection Cohomology of the Symmetric Reciprocal Plane, Preprint, [ttp://pages.uoregon.edu/njp/ukl-m1.pdf PDF], 2015. doi:10.1007/s10801-015-0628-8 ["All three authors would like to acknowledge the On-Line Encyclopedia of Integer Sequences [Slo14], without which this project would have been very difficult."]
  420. Nicholas Proudfoot and Ben Young, Configuration spaces, FSop-modules, and Kazhdan-Lusztig polynomials of braid matroids, arXiv:1704.04510 [math.RT], 2017.
  421. Nicholas Proudfoot, Ben Young, Yuan Xu, The Z-polynomial of a matroid, arXiv:1706.05575 [math.CO], 2017.
  422. Mihai Prunescu, Self-similar carpets over finite fields (2007), arXiv:0708.0899.
  423. Mihai Prunescu and Lorenzo Sauras-Altuzarra, On the representation of C-recursive integer sequences by arithmetic terms, arXiv:2405.04083 [math.LO], 2024. (A000032, A000045, A000051, A000073, A000129, A000225, A000930, A000931, A001045, A001080, A001081, A001477, A001628, A001629, A001872, A001873, A002203, A002249, A007395, A014551, A088137)
  424. Jozef H. Przytycki, History of Knot Theory (2007), arXiv:math/0703096.
  425. W. Pu, J. Choi, E. Amir, Lifted Inference On Transitive Relations, in Workshops at the Twenty-Seventh AAAI Conference on Statistical Relational Artificial Intelligence, 2013.
  426. Jan-Christoph Puchta, The Number of k-Digit Fibonacci Numbers, The Fibonacci Quarterly (2001) Vol. 39, No. 4, 334-335. PDF (A050815)
  427. Lara Pudwell, Digit Reversal Without Apology (2005), arXiv:math/0511366.
  428. Lara Pudwell, Enumeration schemes for permutations avoiding barred patterns, El. J. Combin. 17 (1) (2010) R29.
  429. L. Pudwell, Pattern avoidance in trees (slides from a talk, mentions many sequences), http://faculty.valpo.edu/lpudwell/slides/notredame.pdf, 2012.
  430. L. Pudwell, Avoiding an Ordered Partition of Length 3, 2013; http://faculty.valpo.edu/lpudwell/slides/pp2013pudwell.pdf.
  431. L. K. Pudwell, Ascent sequences and the binomial convolution of Catalan numbers, arXiv preprint arXiv:1408.6823, 2014. Australas J. Comb. 64 (2016) 21-43 PDF
  432. L. Pudwell, Pattern-avoiding ascent sequences, Slides from a talk, 2015; http://faculty.valpo.edu/lpudwell/slides/ascseq.pdf.
  433. Lara Pudwell, On the distribution of peaks (and other statistics), 16th International Conference on Permutation Patterns, Dartmouth College, 2018. PDF (A001263, A091156, A091894, A092107, A236406)
  434. Lara Pudwell, From permutation patterns to the periodic table, Valparaiso University (2019). PDF Also Notices Amer. Math. Soc., 67:7 (2020), 994-1001. (A168380)
  435. L. Pudwell, A. Baxter, Ascent sequences avoiding pairs of patterns, 2014.
  436. Lara Pudwell, Nathan Chenette, Manda Riehl, Statistics on Hypercube Orientations, AMS Special Session on Experimental and Computer Assisted Mathematics, Joint Mathematics Meetings (Denver 2020). PDF (A001787, A001788, A061301)
  437. Pudwell, Lara; Scholten, Connor; Schrock, Tyler; Serrato, Alexa doi:10.1155/2014/316535 Noncontiguous pattern containment in binary trees. ISRN Comb. 2014, Article ID 316535, 8 p. (2014).
  438. Lara Pudwell, Rebecca Smith, Two-stack-sorting with pop stacks, arXiv:1801.05005 [math.CO], 2018. (A224232)
  439. Sílvia Casacuberta Puig, On the divisibility of binomial coefficients, 2018. PDF (A290290, A290203)
  440. Yash Puri and Thomas Ward, "Arithmetic and Growth of Periodic Orbits", J. Integer Sequences, Volume 4, 2001, Article 01.2.1.
  441. Robert James Purser, Mobius Net Cubed-Sphere Gnomonic Grids, U.S. Department of Commerce, National Oceanic and Atmospheric Administration, National Weather Service, National Centers for Environmental Protection, 2018. doi:10.25923/d9rn-fd18 (A008958)
  442. Pushkarev, I. A.; Byzov, V. A. Donaghey's transformation: an elementary approach. (Russian) Zap. Nauchn. Sem. S.-Peterburg. Otdel. Mat. Inst. Steklov. (POMI) 411 (2013), Teoriya Predstavlenii, Dinamicheskie Sistemy, Kombinatornye Metody. XXII, 148--177, 243; translation in J. Math. Sci. (N. Y.) 196 (2014), no. 2, 199-215
  443. B. Putievskiy, Transformations [Of] Integer Sequences And Pairing Functions, arXiv preprint arXiv:1212.2732, 2012.
  444. Boris Putievskiy, Integer Sequences: Irregular Arrays and Intra-Block Permutations, arXiv:2310.18466 [math.CO], 2023.
  445. The Dutch magazine Pythagoras (http://www.pyth.eu/) currently (in 2015) has a series of articles about number sequences, many of which mention the OEIS. Four parts have appeared so far: Een Lexicon vol Getallen ["A Dictionary of Numbers"] (Sept. 2015), Getallenplantjes ["Number plants" (?)] (Oct. 2015), Driehoeksgetallen ["Triangular numbers"] (Nov. 2015), Een bizarre rij [A bizarre sequence] (Dec. 2015).
  446. Pythagoras, Een Eigen Rij - Uitslag Prijsvraag, Nummer 6, Juni 2016, pp. 20-21.
  447. Pythagoras in 2016 had a series of illustrations on the back covers showing sequences from the OEIS. For an example see the January 2016 issue, http://www.pyth.eu/jaargangen/Pyth55-3.pdf

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