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"... every recreational mathematician should buy a copy forthwith." [Martin Gardner, 1974, referring to the Handbook of Integer Sequences]

The talk by Timothy Gowers (2016) mentions the OEIS as a great tool for research, including the fact that he and a collaborator, very recently, were led to a surprising connection.

"On comparing the sequence of cardinalities of these sets with a prepublication version of N. J. A. Sloane's handy table [7], we learned what we should have guessed, that anything which nests is often associated with trees....." [R. K. Guy and J. L. Selfridge, 1973]

About this page

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


  1. Elisabeth Gaar, Daniel Krenn, Metamour-regular Polyamorous Relationships and Graphs, arXiv:2005.14121 [math.CO], 2020. (A000041, A008483, A334275)
  2. Daniel Gabric, Štěpán Holub, Jeffrey Shallit, Generalized de Bruijn words and the state complexity of conjugate sets, arXiv:1903.05442 [cs.FL], 2019. (A316936, A317586)
  3. Daniel Gabric and Joe Sawada, A de Bruijn Sequence Construction by Concatenating Cycles of the Complemented Cycling Register, In: Brlek S., Dolce F., Reutenauer C., Vandomme É. (eds) Combinatorics on Words, WORDS 2017, Lecture Notes in Computer Science, vol 10432. doi:10.1007/978-3-319-66396-8_6
  4. Daniel Gabric, Joe Sawada, Investigating the discrepancy property of de Bruijn sequences, University of Guelph (Canada, 2020). PDF (A008811)
  5. Daniel Gabric, Jeffrey Shallit, Borders, Palindrome Prefixes, and Square Prefixes, arXiv:1906.03689 [cs.DM], 2019. (A003000, A003558, A121880, A122536, A216958, A252696, A308528)
  6. Gabriel, Nathan; Peske, Katherine; Pudwell, Lara; Tay, Samuel, Pattern avoidance in ternary trees. J. Integer Seq. 15 (2012), no. 1, Article 12.1.5, 20 pp.
  7. Steve Gadbois, 104.12 From calendar coincidence to factorials to Ramanujan, The Mathematical Gazette (2020) Vol. 104, Issue 560, 304-306. doi:10.1017/mag.2020.54 (A010790)
  8. Bernd Gaertner, Walter D. Jr. Morris and Leo Ruest, Unique Sink Orientations of Grids, Algorithmica, Volume 51, Number 2 / June, 2008.
  9. Marisa Gaetz, Bethany Flanagan, Marion Scheepers, Meghan Shanks, Quantifying CDS Sortability of Permutations by Strategic Pile Size, arXiv:1811.11937 [math.CO], 2018. (A267323, A267324, A267391, A281259)
  10. Andrei Gagarin, Gilbert Labelle, Pierre Leroux, Timothy Walsh, Structure and enumeration of two-connected graphs with prescribed three-connected components, Advances in Applied Mathematics, Volume 43, Issue 1, July 2009, Pages 46-74.
  11. Franz Gahler and Johan Nilsson, Substitution rules for higher-dimensional paperfolding structures, arXiv:1408.4997, 2014
  12. Ilmar Gahramanov and Edvard T. Musaev, Integrability properties of renormalization group flow, arXiv:1706.00197 [hep-th], 2017.
  13. G. Gaiffi, Nested sets, set partitions and Kirkman-Cayley dissection numbers, arXiv preprint arXiv:1404.3395, 2014
  14. A. Gainer-Dewar, Pólya theory for species with an equivariant group action, arXiv preprint arXiv:1401.6202, 2014. Also Andrew Gainer-Dewar, Species with an equivariant group action, AUSTRALASIAN JOURNAL OF COMBINATORICS, Volume 63(2) (2015), Pages 202–225.
  15. Gainer-Dewar, Andrew; Gessel, Ira M. Counting unlabeled k-trees. J. Combin. Theory Ser. A 126 (2014), 177-193.
  16. K. Gaitanas, An explicit formula for the prime counting function, arXiv preprint arXiv:1311.1398, 2013
  17. D. Galakhov, A. Mironov, A. Morozov, Wall Crossing Invariants: from quantum mechanics to knots, arXiv preprint arXiv:1410.8482, 2014
  18. Pavel Galashin, Periodicity and integrability for the cube recurrence, arXiv:1704.05570 [math.CO], 2017.
  19. Pavel Galashin, Alexander Postnikov, Lauren Williams, Higher secondary polytopes and regular plabic graphs, arXiv:1909.05435 [math.CO], 2019. (A125905)
  20. L. H. Gallardo, On some formulae for Ramanujan's tau function, Rev. Colomb. Matem. 44 (2010) 103-112, HTML
  21. L. H. Gallardo, On a remark of Makowski about perfect numbers, El. Mathem. 65 (3) (2010) 121-126 doi:10.4171/EM/149
  22. LH Gallardo, O Rahavandrainy, There are finitely many even perfect polynomials over F_p with p+1 irreducible divisors, Acta Mathematica Universitatis Comenianae, Vol. 83, No. 2, 2016, 261-275.
  23. Luis H. Gallardo, Olivier Rahavandrainy, On (unitary) perfect polynomials over F_2 with only Mersenne primes as odd divisors, arXiv:1908.00106 [math.NT], 2019. (A000043, A00668, A007691)
  24. RR Gallyamov, IR Kadyrov, DD Kashelevskiy, A fast modulo primes algorithm for searching perfect cuboids and its implementation, arXiv preprint arXiv:1601.00636, 2016
  25. P. Gambette, V. Berry, C. Paul, The structure of level-k phylogenetic networks, LNCS 5577 (2009) 289-300 doi:10.1007/978-3-642-02441-2_26
  26. K. R. R. Gandhi, Edifice of the real numbers by alternating series, International Journal of Mathematical Archive-3(9), 2012, 3277-3280.
  27. A. Ganesan, Automorphism groups of graphs, Arxiv preprint arXiv:1206.6279, 2012.
  28. Karthik Ganesan, Alexander Hu, Subhasish Mitra, H.-S. Philip Wong, Simon Wong, Tony F. Wu, TPAD: Hardware Trojan Prevention and Detection for Trusted Integrated Circuits, preprint arXiv:1505.02211, 2015. (A011260)
  29. Mohammad GANJTABESH, Armin MORABBI and Jean-Marc STEYAERT, Enumerating the number of RNA structures
  30. Bernhard Ganter, Sergei Obiedkov, An algorithm for closure systems, in Conceptual Exploration, Springer 2016, Pages pp 39-85, doi:10.1007/978-3-662-49291-8_2
  31. A. L. L. Gao, E. X. L. Gao, P. Laborde-Zubieta, and B. Y. Sun, Enumeration of Corners in Tree-like Tableaux and a Conjectural (a,b)-analogue, arXiv preprint arXiv:1511.05434, 2015.
  32. Alice L. L. Gao, Sergey Kitaev, On partially ordered patterns of length 4 and 5 in permutations, arXiv:1903.08946 [math.CO], 2019. (A000984, A002605, A006012, A006318, A007531, A025192, A033321, A045925, A048495, A049124, A052544, A053617, A054872, A057711, A077835, A084509, A094012, A094433, A103505, A106228, A111277, A111279, A111281, A111282, A118376, A128088, A129952, A165546, A204200, A212198, A214663, A216879, A224295, A228907, A232164, A257561, A271897, A276838)
  33. Alice L. L. Gao, S Kitaev, PB Zhang, On pattern avoiding indecomposable permutations, arXiv preprint arXiv:1605.05490, 2016.
  34. Emily X. L. Gao and Brian Y. Sun, Enumeration of Type D Permutations with Alternating Runs, Preprint 2017.
  35. Emma L. L. Gao, Sergey Kitaev, Philip B. Zhang, Pattern-avoiding alternating words, preprint, 2015. (A000045, A006356, A006357, A006358, A006359)
  36. M. Gao and J. Wu, Homology Decompositions of the Loops on 1-Stunted Borel Constructions of C_2-Actions, arXiv preprint arXiv:1301.0864, 2013
  37. Gao, Shanzhen, and Matheis, Kenneth, Closed formulas and integer sequences arising from the enumeration of (0,1)-matrices with row sum two and some constant column sums. In Proceedings of the Forty-First Southeastern International Conference on Combinatorics, Graph Theory and Computing. Congr. Numer. 202 (2010), 45-53.
  38. Shanzhen Gao and Heinrich Niederhausen, Sequences Arising From Prudent Self-Avoiding Walks, Preprint, 2010.
  39. Si Gao, H Chen, W Wu, L Fan, W Cao, X Ma, My traces learn what you did in the dark: recovering secret signals without key guesses, Preprint, 2016,
  40. Xiangrui Gao, Song He, Yong Zhang, Labelled tree graphs, Feynman diagrams and disk integrals, arXiv:1708.08701 [hep-th], 2017.
  41. Yibo Gao, Principal specializations of Schubert polynomials and pattern containment, arXiv:1910.08872 [math.CO], 2019. (A005043)
  42. Gao, Zhicheng; MacFie, Andrew; Panario, Daniel Counting words by number of occurrences of some patterns. Electron. J. Combin. 18 (2011), no. 1, Paper 143, 15 pp.
  43. Zhicheng Gao, Andrew MacFie and Daniel Panario, Counting words by number of occurrences of some patterns, The Electronic Journal of Combinatorics, 18 (2011), #p143;
  44. Xing Gao & William F. Keigher, Interlacing of Hurwitz series, Communications in Algebra, 45:5 (2017), 2163-2185, doi:10.1080/00927872.2016.1226885
  45. S. Garoufalidis and R. Kashaev, From state integrals to q-series, arXiv preprint arXiv:1304.2705, 2013
  46. Jozsef Garai, Analytical Solution Describing the Periodicity of the Elements in the Periodic System (2007), arXiv:physics/0703231.
  47. Alexey Garber, On triangular paperfolding patterns, arXiv:1807.05627 [math.CO], 2018. (A014577)
  48. Mariano Garcia, "A Million New Amicable Pairs", J. Integer Sequences, Volume 4, 2001, Article 01.2.6.
  49. E. M. García-Caballero, S. G. Moreno, M. P. Prophet, A complete view of Viète-like infinite products with Fibonacci and Lucas numbers, Applied Mathematics and Computation 247 (2014) 703–711.
  50. E. M. García-Caballero, S. G. Moreno, M. P. Prophet, New Viète-like infinite products of nested radicals, Fib. Q., 52 (No. 1, 2014), 27-31.
  51. Ana Cecilia García Lomelí, Santos Hernández Hernández, Repdigits as Sums of Two Padovan Numbers, J. Int. Seq., Vol. 22 (2019), Article 19.2.3. HTML (A000931)
  52. M. I. García-Planas and D. Roca-Borrego, Cyclic-union Operation to Obtain Latin Squares, British Journal of Mathematics & Computer Science, Vol. 22, Issue. 5, 2017. doi:10.9734/BJMCS/2017/33945
  53. P. A. García-Sánchez, D. Marín-Aragón, A. M. Robles-Pérez, The tree of numerical semigroups with low multiplicity, arXiv:1803.06879 [math.CO], 2018.
  54. Martin Gardner, Mathematical Games column, Scientific American, July 1974, referring to the Handbook of Integer Sequences, said that “every recreational mathematician should buy a copy forthwith.”
  55. Martin Gardner, Penrose Tiles to Trapdoor Ciphers, Freeman, NY, 1989. See p. 21.
  56. M. R. Garey, On enumerating tournaments that admit exactly one Hamiltonian circuit, J. Combin. Theory, B 13 (1972), 266-269. [R. J. Douglas had enumerated such tournaments. In collecting sequences for the 1973 book I noticed that these numbers were a bisection of the Fibonacci numbers and my colleague Mike Garey found a proof of this.]
  57. Skip Garibaldi, "Somewhat more than governors need to know about trigonometry", Mathematics Magazine, vol. 81, No. 3, (2008) pp. 191-200.
  58. S. M. Garrabrant, P-recursive integer sequences and automata theory, Thesis (2015) UCLA
  59. S. Garrabrant, I. Pak, Counting with irrational tiles, arXiv:1407.8222, 2014.
  60. Scott Garrabrant, Igor Pak, Pattern Avoidance is Not P-Recursive, preprint, 2015. (A111111, A003216, A000088)
  61. S. Garrabrant, I. Pak, Words in linear groups, computability and p-recursiveness, 2015; arXiv:1502.06565
  62. Scott Garrabrant, I Pak, Permutation patterns are hard to count, Proceedings of SODA '16, the Twenty-Seventh Annual ACM-SIAM, Symposium on Discrete Algorithms, Pages 923-936.
  63. James Garrett, Nataša Jonoska, Hwee Kim, Masahico Saito, DNA Origami Words and Rewriting Systems, International Conference on Unconventional Computation and Natural Computation (UCNC 2019) Lecture Notes in Computer Science, vol 11493. Springer, Cham, 94-107. doi:10.1007/978-3-030-19311-9_9
  64. T. Garrity, A Multidimensional Continued Fraction Generalization of Stern's Diatomic Sequence, J. Int. Seq. 16 (2013) #13.7.7
  65. A. Garsia, J. Haglund, A polynomial expression for the character of diagonal harmonics, 2014;
  66. Adriano M. Garsia, James Haglund, Dun Qiu, Marino Romero, e-Positivity Results and Conjectures, arXiv:1904.07912 [math.CO], 2019. (A001187)
  67. David Garth and Adam Gouge, "Affinely Self-Generating Sets and Morphisms", J. Integer Sequences, Volume 10, 2007, Article 07.1.5.
  68. David Garth, Donald Mills and Patrick Mitchell, "Polynomials Generated by the Fibonacci Sequence", J. Integer Sequences, Volume 10, 2007, Article 07.6.8.
  69. Garvan, F. G. Higher order spt-functions. Adv. Math. 228 (2011), no. 1, 241-265.
  70. Frank G. Garvan, Congruences and relations for r-Fishburn numbers, arXiv:1406.5611, 2014. Also Preprint, March 12 2015;
  71. Alexander Garver, Thomas McConville, Chapoton triangles for nonkissing complexes, University of Michigan (2020). [ PDF] (A060854)
  72. William Gasarch, Clyde Kruskal, Problems With A Point: Exploring Math And Computer Science, World Scientific, 2018, p. 44. Abstract
  73. T. Alden Gassert, Discriminants of simplest 3^n-tic extensions, arXiv preprint arXiv:1409.7829, 2014
  74. Nicolas Gastineau, O Togni, On S-packing edge-colorings of cubic graphs, arXiv preprint arXiv:1711.10906, 2017
  75. Nicolas Gastineau, Olivier Togni, Coloring of the dth power of the face-centered cubic grid, arXiv:1806.08136 [cs.DM], 2018. (A005902)
  76. N. Gast, B. Gaujal, Infinite labeled trees: from rational to Sturmian trees, Theor. Comput. Sci. 411 (2010) 1146-1166 doi:0.1016/j.tcs.2009.12.009
  77. Victoria Gatt, Mikhail Klin, Josef Lauri, Valery Liskovets, From Schur Rings to Constructive and Analytical Enumeration of Circulant Graphs with Prime-Cubed Number of Vertices, in Isomorphisms, Symmetry and Computations in Algebraic Graph Theory, (Pilsen, Czechia, WAGT 2016) Vol. 305, Springer, Cham, 37-65. doi:10.1007/978-3-030-32808-5_2 (A000171, A001003, A049297, A056391)
  78. W. Gatterbauer, D. Suciu, Approximate Lifted Inference with Probabilistic Databases, arXiv preprint arXiv:1412.1069, 2014
  79. Wolfgang Gatterbauer, Dan Suciu, Dissociation and propagation for approximate lifted inference with standard relational database management systems, The VLDB Journal, February 2017, Volume 26, Issue 1, pp 5–30; doi:10.1007/s00778-016-0434-5
  80. D. Gault and M. Clint, "Curiouser and curiouser" said Alice. Further reflections on an interesting recursive function, Internat. J. Computer Math., 26 (1988), 35-43.
  81. N. Gauthier (Proposer), Problem H-703, Fib. Quart., 50 (2012), 379-381.
  82. Thibault Gauthier, Deep Reinforcement Learning for Synthesizing Functions in Higher-Order Logic, arXiv:1910.11797 [cs.AI], 2019. See also EPiC Series in Computing (2020) Vol. 73, 230-248. doi:10.29007/7jmg (A001652)
  83. Nicolas Gauvrit, Jean-Paul Delahaye and Hector Zenil, Le fosse de Sloane
  84. Nicolas Gauvrit, Jean-Paul Delahaye and Hector Zenil, Sloane's Gap: Do Mathematical and Social Factors Explain the Distribution of Numbers in the OEIS? - arXiv:1104.4470, J. Human. Math 3 (2013) #1, HTML
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  87. Vladimir L. Gavrikov, On property of least common multiple to be a D-magic number, arXiv:1806.09264 [math.NT], 2018. (A003418)
  88. Volodymyr Gavrylkiv and Taras Banakh, Difference bases in cyclic groups, ResearchGate, 2017.
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  90. P. Gawrychowski, P. K. Nicholson, Optimal Encodings for Range Top-k, Selection, and Min-Max, arXiv preprint arXiv:1411.6581, 2014. Also in Automata, Languages, and Programming, Volume 9134 of the series Lecture Notes in Computer Science, 2015, pp. 593-604.
  91. Joël Gay, Representation of Monoids and Lattice Structures in the Combinatorics of Weyl Groups, Doctoral Thesis, Discrete Mathematics [cs.DM], Université Paris-Saclay, 2018. Abstract (A000295, A001047, A003121, A121079, A121080)
  92. Joël Gay, Vincent Pilaud, The weak order on Weyl posets, arXiv:1804.06572 [math.CO], 2018. (A000079, A000108, A000142, A000165, A000244, A000260, A000670, A000798, A000984, A001003, A001035, A001850, A002866, A006455, A007767, A047656, A051924, A053764, A060722, A080253, A080254)
  93. Dmitry Gayfulin, Nikita Shulga, Diophantine properties of fixed points of Minkowski question mark function, arXiv:1811.10139 [math.NT], 2018. (A058914)
  94. Volker Gebhardt and Stephen Tawn, Constructing unlabelled lattices, arXiv:1609.08255, 2016.
  95. Fekadu T. Gedefa, Log-Concavity of Centered Polygonal Figurate Number Sequences, Open Access Library Journal, 2016, 3: e2774. doi:10.4236/oalib.1102774
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  97. Katie R. Gedeon, Kazhdan-Lusztig polynomials of thagomizer matroids, arXiv preprint arXiv:1610.05349, 2016 ["The success of this project is due in large part to the On-Line Encyclopedia of Integer Sequences [Slo16] and SageMath [Dev16]."]
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  100. Thangavelu Geetha, Amritanshu Prasad, Shraddha Srivastava, Schur Algebras for the Alternating Group and Koszul Duality, arXiv:1902.02465 [math.RT], 2019. (A002860)
  101. Ivan Geffner, Marc Noy, Counting Outerplanar Maps, Electronic Journal of Combinatorics 24(2) (2017), #P2.3
  102. Daniel L. Geisler, Combinatorics of Iterated Functions
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  138. S. K. Ghosal, J. K. Mandal, Stirling Transform Based Color Image Authentication, Procedia Technology, 2013 Volume 10, 2013, Pages 95-104.
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  145. Philip Gibbs, Judson McCranie, The Ulam Numbers up to One Trillion, 2017. PDF (A000930, A002858, A072540, A080287, A080288)
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  148. Jan de Gier and Bernard Nienhuis, Brauer loops and the commuting variety (2004), arXiv:math/0410392.
  149. Christian Gießen, Monotone Functions on Bitstrings – Some Structural Notes, Theory of Randomized Optimization Heuristics, Dagstuhl Seminar 17191 (2017), 3.12, p. 33. PDF (A000372)
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  462. Guy R. K., doi:10.1016/S0898-1221(00)00123-1 Problems sessions 92-05-29 and 92-05-31, Computers & Mathematics with Applications, Volume 39, Issue 11, June 2000, Pages 169-171.
  463. R. K. Guy, Unsolved Problems in Number Theory. Springer, 3rd edition, 2004, ISBN 978-0387208602.
  464. Richard K. Guy, "What's Next?" in "The Edge of the Universe: Celebrating Ten Years of Math Horizons" edited by D. Haunsperger and S. Kennedy, pages 81-83 (2004) ISBN: 978-0883855553
  465. Richard K. Guy, Unsolved Problems in Number Theory, 3rd ed., Springer 2010.
  466. R. K. Guy and T. Khovanova, Conway's subprime Fibonacci sequences, Arxiv preprint arXiv:1207.5099, 2012
  467. R. K. Guy, C. Krattenthaler and B. E. Sagan, Lattice paths, reflections and dimension-changing bijections, Ars Combin. 34 (1992), 3-15.
  468. R. K. Guy and W. O. J. Moser, Numbers of subsequences without isolated odd members. Fibonacci Quarterly, 34, No.2, 152-155 (1996).
  469. R. K. Guy and R. J. Nowakowski, Mousetrap, Preprint, Feb 10 1993
  470. R. K. Guy and J. L. Selfridge, The nesting and roosting habits of the laddered parenthesis. Amer. Math. Monthly 80 (1973), 868-876. "On comparing the sequence of cardinalities of these sets with a prepublication version of N. J. A. Sloane's handy table [7], we learned what we should have guessed, that anything which nests is often associated with trees...."
  471. René Gy, Extended Congruences for Harmonic Numbers, arXiv:1902.05258 [math.NT], 2019. (A001220)
  472. M. Gysin and J. Seberry, On infinite families of sequences with one and two valued autocorrelation and two valued crosscorrelation function, AJC 23 (2001) 197-209.

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