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"The OEIS database [144] was very helpful." [Martin Klazar, 2018]

"the authors also want to thank the On-Line Encyclopedia of Integer Sequences (OEIS) [25] for being a helpful resource in identifying the Bernoulli numbers as coefficients in Eq. (3)." [P. Knechtges et al., 2014]

"... again it reports a case where I discovered a new mathematical result thanks to OEIS. In fact, I think this case might well be the best ever in my experience so far." [D. E. Knuth, 2020]

"... among databases, the "Online Encyclopedia of Integer Sequences" (OEIS) focuses on sequences over Z and their properties." [Michael Kohlhase et al., 2017]

"Thanks are ... due to all contributors and editors of the websites and" [Alexei Kourbatov, 2017]

"We would not have discovered this connection between quantum mechanical experiments and graph theory, thus the physical interpretations and all the generalisations we are developing right now, without you and A000438." [Mario Krenn et al., 2017]

About this page

  • This is part of the series of OEIS Wiki pages that list works citing the OEIS.
  • Additions to these pages are welcomed.
  • But if you add anything to these pages, please be very careful — remember that this is a scientific database. Spell authors' names, titles of papers, journal names, volume and page numbers, etc., carefully, and preserve the alphabetical ordering.
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  • Works are arranged in alphabetical order by author's last name.
  • Works with the same set of authors are arranged by date, starting with the oldest.
  • This section lists works in which the first author's name begins with K.
  • 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. Z Kabluchko, V Vysotsky, D Zaporozhets, Convex hulls of random walks, hyperplane arrangements, and Weyl chambers, arXiv preprint arXiv:1510.04073, 2015
  2. Yasuyuki Kachi and Pavlos Tzermias, Infinite products involving zeta(3) and Catalan's constant, Journal of Integer Sequences, Vol. 15 (2012), #12.9.4.
  3. Y Kachi, P Tzermias, On the m-ary partition numbers, Algebra and Discrete Mathematics, Volume 19 (2015). Number 1, pp. 67–76.
  4. O. A. Kadubovskyi, Enumeration of 2-color chord diagrams of maximal genus under rotation and reflection, Conference: Sixteenth International Scientific Mykhailo Kravchuk Conference, At Kyiv, Volume: Vol. 2. Algebra. Geometry. Analysis, 2015. (A001171)
  5. Shirali Kadyrov, Farukh Mashurov, Generalized continued fraction expansions for π and e, arXiv:1912.03214 [math.NT], 2019. (A000166, A001710, A182386)
  6. Bir Kafle et al., Triangular repblocks, Fib. Q., 56:4 (2018), 325-328.
  7. Bir Kafle, Florian Luca, Alain Togbé, X-coordinates of Pell equations which are Lucas numbers, Boletín de la Sociedad Matemática Mexicana (2018), 1-13. doi:10.1007/s40590-018-0221-y
  8. B. Kafle, A. Srinivasan, and A. Togbé, Markov equation with Pell components, Fib. Q., 58:3 (2020), 226-230.
  9. Jonas Kaiser, On the relationship between the Collatz conjecture and Mersenne prime numbers, arXiv preprint arXiv:1608.00862, 2016
  10. T. Kaiser and M. Klazar, On growth rates of hereditary permutation classes, Electr. J. Combinatorics 9 (2) (2003), R10, 20 pages.
  11. Shizuo Kaji, A Derouet-Jourdan, H Ochiai, Dappled tiling, arXiv preprint arXiv:1607.06138, 2016
  12. S. Kaji, T. Maeno, K. Nuida, Y. Numata, arXiv:1506.02742 Polynomial Expressions of Carries in p-ary Arithmetics, arXiv preprint, 2015. (A00037, A002445)
  13. E. Kalinowski and W. Gluza, Evaluation of high-order terms for the Hubbard model in the strong-coupling limit, Phys. Rev. B 85 (4), 045105 (2012), 8 pages, doi:10.1103/PhysRevB.85.045105. Also arXiv:1106.4938, 2011.
  14. Burton S Kaliski Jr, Targeted Fibonacci Exponentiation, arXiv preprint arXiv:1711.02491, 2017.
  15. Myrto Kallipoliti, Robin Sulzgruber, Eleni Tzanaki, Patterns in Shi tableaux and Dyck paths, arXiv:2006.06949 [math.CO], 2020. (A000079, A000124, A080934, A114702, A116847)
  16. Kallós, Gábor, A generalization of Pascal's triangle using powers of base numbers, Ann. Math. Blaise Pascal 13 (2006), no. 1, 1-15.
  17. E. Kalvelagen, Tiling Squares.
  18. E. Kalvelagen, New special functions in GAMS
  19. Ken Kamano, Sums of Products of Poly-Bernoulli Numbers of Negative Index, Journal of Integer Sequences, Vol. 15 (2012), #12.1.3.
  20. G. A. Kamel. Partial Chain Topologies on Finite Sets. Computational and Applied Mathematics Journal. Vol. 1, No. 4, 2015, pp. 174-179.
  21. Dmitry Kamenetsky, Prime Sums of Primes, arXiv:1703.06778 [math.HO], 2017.
  22. Kamioka, Shuhei, A combinatorial representation with Schroeder paths of biorthogonality of Laurent biorthogonal polynomials. Electron. J. Combin. 14 (2007), no. 1, Research Paper 37, 22 pp.
  23. S. Kamioka, Laurent biorthogonal polynomials, q-Narayana polynomials and domino tilings of the Aztec diamonds, arXiv preprint arXiv:1309.0268, 2013 doi:10.1016/j.jcta.2013.11.002, J. Combin. Theory A 123 (2014) 14-19.
  24. S. Kamioka, T. Takagaki, Combinatorial expressions of the solutions to initial value problems of the discrete and ultradiscrete Toda molecules, arXiv preprint arXiv:1303.4173, 2013
  25. Y. Kamiyama, On the middle dimensional homology classes of equilateral polygon spaces, arXiv preprint arXiv:1507.03161, 2015
  26. Yasuhiko Kamiyama, The Euler characteristic of the regular spherical polygon spaces, arXiv:1803.05559 [math.GT], 2018. (A000531)
  27. Takeo Kamizawa, Note on the Distance to the Nearest Integer
  28. Daniel M Kane, Asymptotic Results for the Queen Packing Problem, arXiv:1703.04538 [math.CO], 2017.
  29. Daniel Kane and Robert C. Rhoades, Asymptotics For Wilf's Partitions with Distinct Multiplicities, PDF.
  30. Daniel M. Kane, Carlo Sanna, Jeffrey Shallit, Waring's Theorem for Binary Powers, arXiv:1801.04483 [math.NT], 2018. (A020330, A297405)
  31. Masanobu Kaneko, "The Akiyama-Tanigawa algorithm for Bernoulli numbers", J. Integer Sequences, Volume 3, 2000, Article 00.2.9.
  32. Lucas Kang, Investigation of Rule 73 as Case Study of Class 4 Long-Distance Cellular Automata, arXiv preprint arXiv:1310.3311, 2013
  33. Kairi Kangro, M. Pourmoradnasseri, and D. O. Theis, Short note on the number of 1-ascents in dispersed Dyck paths, arXiv preprintarXiv:1603.01422, 2016
  34. C Kankanamge, Multiple Continuous Subgraph Query Optimization Using Delta Subgraph Queries, Master of Mathemematics in Computer Science, Thesis, Univ. Waterloo, 2018.
  35. S. R. Kannan, Rajesh Kumar Mohapatra, Counting the Number of Non-Equivalent Classes of Fuzzy Matrices Using Combinatorial Techniques, arXiv:1909.13678 [math.GM], 2019. (A002416, A328044)
  36. Craig S. Kaplan, Grid-based decorative corners, in Proceedings of Bridges 2013: Mathematics, Music, Art, ..., 2013;
  37. H. Kaplan, R. Shamir and R. E. Tarjan, Tractability of parameterized completion problems on chordal, strongly chordal and proper interval graphs, SIAM Journal of Computing 28(5) 1906-1922 (1999), doi:10.1137/S0097539796303044.
  38. Anatolii A. Karatsuba and Ekatherina A. Karatsuba, The "problem of remainders" in theoretical physics: "physical zeta" function,
  39. Karatsuba, Anatolii A.; Karatsuba, Ekatherina A. Physical mathematics in number theory. Funct. Anal. Other Math. 3 (2011), no. 2, 113-125.
  40. M. I. Karavelas, C. Konaxis and E. Tzanaki, The maximum number of faces of the Minkowski sum of three convex polytopes, arXiv preprint arXiv:1211.6089, 2012
  41. Maksim Karev, The space of framed chord diagrams as a Hopf module, arXiv preprint arXiv:1404.0026, 2014
  42. Juhani Karhumaki, Yury Lifshits and Wojciech Rytter, Tiling Periodicity, in Combinatorial Pattern Matching, Lecture Notes in Computer Science, Volume 4580/2007, Springer-Verlag PDF.
  43. Juhani Karhumäki, S Puzynina, M Rao, MA Whiteland, On cardinalities of k-abelian equivalence classes, arXiv preprint arXiv:1605.03319, 2016
  44. Juhani Karhumäki, Markus A. Whiteland, Regularity of k-Abelian Equivalence Classes of Fixed Cardinality, Adventures Between Lower Bounds and Higher Altitudes, Lecture Notes in Computer Science, Vol. 11011, Springer, Cham, 49-62. doi:10.1007/978-3-319-98355-4_4 (A289657, A289658)
  45. Katarzyna Karnas and Adam Sawicki, Products of finite order rotations and quantum gates universality, arXiv:1704.03887 [quant-ph], 2017.
  46. D. Karp and E. Prilepkina, Generalized Stieltjes transforms: basic aspects, Arxiv preprint arXiv:1111.4271, 2011
  47. D. Karp and E. Prilepkina, Generalized Stieltjes functions and their exact order, Journal of Classical Analysis Volume 1, Number 1 (2012), 53-74, PDF
  48. Alexander V. Karpov, An Informational Basis for Voting Rules, 2018. PDF (A001399, A005513, A037240, A257464)
  49. Alexander Karpov, On the Number of Group-Separable Preference Profiles, Group Decision and Negotiation (2019), Vol. 28, Issue 3, 501–517. doi:10.1007/s10726-019-09621-w
  50. Dimitrios Kartsaklis, Sanjaye Ramgoolam, Mehrnoosh Sadrzadeh, Linguistic Matrix Theory, arXiv:1703.10252 [cs.CL], 2017.
  51. A. Karttunen, Introductory Survey of Catalan Automorphisms
  52. A. Karttunen, On Pascal's Triangle Modulo 2 in Fibonacci Representation, The Fibonacci Quarterly, Vol. 42, 1 (February 2004) pp. 38-46.
  53. A. Karttunen, "Tuhansien lukujonojen aarreaitta" [A treasure-trove of thousands of integer sequences], Helsingin Sanomat, Science and Nature Section, page D1, November 9 2004.
  54. Z. Kasa, On scattered subword complexity, Arxiv preprint arXiv:1104.4425, 2011.
  55. Z. Kasa and Z. Katai Scattered subwords and composition of natural numbers, Acta Univ. Sapientiae, Informatica, 4, 2 (2012) 225-236 PDF.
  56. Kashyap, Navin; Siegel, Paul H.; and Vardy, Alexander, An application of Ramsey theory to coding for the optical channel. SIAM J. Discrete Math. 19 (2005), no. 4, 921-937 doi:10.1137/S089548010444585X.
  57. C. Kassel, On combinatorial zeta functions, Slides from a talk, Potsdam, 2015:
  58. C. Kassel and C. Reutenauer, Algebraicity of the zeta function associated to a matrix over a free group algebra, arXiv preprint arXiv:1303.3481, 2013
  59. Christian Kassel, Christophe Reutenauer, On the zeta functions of punctual Hilbert schemes of a two-dimensional torus, arXiv:1505.07229 [math.AG] [Note that version 1 mentions the OEIS 16 times. Later versions of this paper have a different title and different contents.]
  60. Christian Kassel, C Reutenauer, Complete determination of the zeta function of the Hilbert scheme of n points on a two-dimensional torus, arXiv preprint arXiv:1610.07793, 2016
  61. Christian Kassel, Christophe Reutenauer, The Fourier expansion of eta(z)eta(2z)eta(3z)/eta(6z), Archiv der Mathematik, May 2017, Volume 108, Issue 5, pp. 453-463. doi:10.1007/s00013-017-1033-4. Preprint: arXiv:1603.06357 [math.NT], 2016.
  62. Thomas Boyer-Kassem, Conor Mayo-Wilson, Scientific Collaboration and Collective Knowledge: New Essays, New York, Oxford University Press, 2018, see page 47. (A000088)
  63. Jeremy Kastine, Maximally Even Tilings, International Conference on Mathematics and Computation in Music (MCM 2019), Lecture Notes in Computer Science, Vol. 11502, Springer, Cham, 309-321. doi:10.1007/978-3-030-21392-3_25 (A102562)
  64. Lars Kastner, Marta Panizzut, Hyperplane arrangements in polymake, arXiv:2003.13548 [math.CO], 2020. (A034997)
  65. András Kaszanyitzky, Triangular fractal approximating graphs and their covering paths and cycles, arXiv:1710.09475 [math.CO], 2017. (A067771, A112676)
  66. András Kaszanyitzky, The GraftalLace Cellular Automaton. arXiv:1805.11532 [nlin.CG], 2018. (A000085)
  67. Go Kato, Shin-ichi Minato, Enumeration of associative magic squares of order 7, arXiv:1906.07461 [math.CO], 2019. (A081262)
  68. J. Katriel, On a generalized recurrence for Bell Numbers, JIS 11 (2008) 08.3.8
  69. U. N. Katugampola, A new Fractional Derivative and its Mellin Transform, Arxiv preprint arXiv:1106.0965, 2011
  70. U. N. Katugampola, Mellin Transforms of the Generalized Fractional Integrals and Derivatives, Arxiv preprint arXiv:1112.6031, 2011
  71. U. N. Katugampola, Existence and Uniqueness results for a class of Generalized Fractional Differential Equations, arXiv preprint arXiv:1411.5229, 2014
  72. M. Katz, C. Stenson, Tiling a 2Xn-board witih squares and dominoes, JIS 12 (2009) 09.2.2
  74. Kauers, Manuel, SumCracker: a package for manipulating symbolic sums and related objects. J. Symbolic Comput. 41 (2006), no. 9, 1039-1057.
  75. M. Kauers, An algorithm for deciding zero equivalence of nested polynomially recurrent sequences, ACM Trans. Algorithms 3 (2) (2007) # 18, doi:10.1145/1240233.1240241
  76. M. Kauers, The Holonomic Toolkit,, 2013. Texts and Monographs in Symbolic Computation, 119-144 (2013) doi:10.1007/978-3-7091-1616-6_5.
  77. Manuel Kauers, Christoph Koutschan and Doron Zeilberger, Proof of Ira Gessel's Lattice Path Conjecture (2008); arXiv:0806.4300
  78. M. Kauers, C. Koutschan and D. Zeilberger, doi:10.1073/pnas.0901678106 Proof of Ira Gessel's lattice path conjecture, Proc Natl. Acad. Sci. 106 (28) (2009) pp 11502-11505.
  79. Manuel Kauers, Jakob Moosbauer, Good pivots for small sparse matrices, arXiv:2006.01623 [cs.SC], 2020. (A002724)
  80. M. Kauers and P. Paule, The Concrete Tetrahedron, Springer 2011.
  81. Manuel Kauers and Doron Zeilberger, The Computational Challenge of Enumerating High-Dimensional Rook Walks
  82. Manuel Kauers, Doron Zeilberger, Counting Standard Young Tableaux With Restricted Runs, arXiv:2006.10205 [math.CO], 2020. (A000045, A000085, A000108, A001006)
  83. Manuel Kauers and Burkhard Zimmermann, Computing the algebraic relations of C-finite sequences and multisequences, Journal of Symbolic Computation, Volume 43, Issue 11, November 2008, Pages 787-803.
  84. L. H. Kauffman, Non-Commutative Worlds-Classical Constraints, Relativity and the Bianchi Identity, Arxiv preprint arXiv:1109.1085, 2011 [The sequence mentioned is A050534]
  85. Steven M. Kautz, James I. Lathrop, Self-assembly of the discrete Sierpinski carpet and related fractals (2009) arXiv:0901.3189
  86. Jun Kawahara, Takashi Horiyama, Keisuke Hotta, Shin-ichi Minato, Generating All Patterns of Graph Partitions Within a Disparity Bound, In: Poon SH., Rahman M., Yen HC. (eds) WALCOM: Algorithms and Computation, WALCOM 2017, Lecture Notes in Computer Science, vol 10167, pp. 119-131. doi:10.1007/978-3-319-53925-6_10
  87. Jun Kawahara, Toshiki Saitoh, Ryo Yoshinaka and Shin-ichi Minato, Counting Primitive Sorting Networks by pi-DDs, TCS-TR-A-11-54 TCS Technical Report ', Science Report Series A October 17, 2011 Hokkaido University;
  88. Bernd Kawohl and Christof Weber, Meissner's Mysterious Bodies, Mathematical Intelligencer, Volume 33, Number 3, 2011, pp. 94-101.
  89. Rene Kay, Todd Kay, Planet Seeker Interferometer (PSI), hal-02870885v2 [astro-ph.IM], 2020. Abstract (A245461)
  90. George Kaye, A visualiser for linear λ-terms as 3-valent rooted maps, University of Birmingham (UK, 2019). PDF (A062980)
  91. L. Kaylor and D. Offner, Counting Matrices Over a Finite Field With All Eigenvalues in the Field, 2013;
  92. S Kechrimparis, S Weigert, Universality in Uncertainty Relations for a Quantum Particle, arXiv preprint arXiv:1509.02146, 2015
  93. Kiran S. Kedlaya and Andrew V. Sutherland, Computing L-series of hyperelliptic curves (2008); arXiv:0801.2778; in Algorithmic Number Theory, Lecture Notes in Computer Science, Volume 5011/2008, Springer-Verlag.
  94. Chris Keeler, New metrics for finite automaton complexity and subregular language hierarchies. Master's Thesis, School of Computing, Queen's University. Kingston, Ontario. 2017.
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  123. Keskin, Refik; Karaatli, Olcay, Some new properties of balancing numbers and square triangular numbers. J. Integer Seq. 15 (2012), no. 1, Article 12.1.4, 13 pp.
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  128. Sameen Ahmed Khan, The bounds of the set of equivalent resistances in n-equal transistors combined in series and in parallel, arXiv:1004.3346 April 2010.
  129. S. A. Khan, Primes in Geometric-Arithmetic Progression, Arxiv preprint arXiv:1203.2083, March 2012.
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  142. Anton Khoroshkin, Thomas Willwacher, Real moduli space of stable rational curves revisted, arXiv:1905.04499 [math.AT], 2019. (A001003)
  143. Oleksiy Khorunzhiy, On asymptotic behavior of Bell polynomials and high moments of vertex degree of random graphs, arXiv:1904.01339 [math.PR], 2019.
  144. Tanya Khovanova, How to Create a New Integer Sequence, arXiv:0712.2244. Also
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  149. Tanya Khovanova, Attacking ApSimon's Mints, arXiv:1406.3012, 2014.
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  151. Tanya Khovanova, Coins and Logic, arXiv preprint arXiv:1801.01143, 2018. See also "Coins and Logic", Chapter 6, The Mathematics of Various Entertaining Subjects: Volume 3 (2019), Jennifer Beineke & Jason Rosenhouse, eds. Princeton University Press, Princeton and Oxford, p. 73. ISBN: 0691182582, 978-0691182582. (A001045)
  152. T. Khovanova, K. Knop, Coins of Three Different Weights, arXiv preprint arXiv:1410.0250, 2014
  153. Tanya Khovanova, K Knop, Coins that Change Their Weights, arXiv preprint arXiv:1611.09201, 2016
  154. T. Khovanova, K. Knop, A. Radul, Baron Munchhausen's Sequence, J. Int. Seq. 13 (2010) # 10.8.7
  155. Khovanova, Tanya; Lewis, Joel Brewster, Baron Münchhausen redeems himself: bounds for a coin-weighing puzzle. Electron. J. Combin. 18 (2011), no. 1, Paper 37, 14 pp.
  156. T. Khovanova and J. B. Lewis, Skyscraper Numbers, arXiv preprint arXiv:1304.6445, 2013 and J. Int. Seq. 16 (2013) #13.7.2
  157. T. Khovanova and D. Yang, Halving Lines and Their Underlying Graphs, arXiv preprint arXiv:1210.4959, 2012
  158. T. Khovanova, D. Yang, Fission of Halving Edges Graphs, arXiv preprint arXiv:1310.3510, 2013
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