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"JM thanks Karol Penson for introducing to him a wonderful world of the On-Line Encyclopedia of Integer Sequences..." [Aernout van Enter et al., 2019]

"We tested this on numerous differential equations obtained from the (the Online Encyclopedia of Integer Sequences)." [Mark van Hoeij and VJ Kunwar, 2019]

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 V.
  • 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. Daniel Vainsencher, Alfred M. Bruckstein, On isoperimetrically optimal polyforms, Theoretical Computer Science, Volume 406, Issues 1-2, 28 October 2008, Pages 146-159.
  2. Robert Vajda, Exploring Hermite interpolation polynomials using recursion, Annales Mathematicae et Informaticae, 45 (2015) pp. 151–160;
  3. Robert Vajda, Computational Exploration of the Degree Sequence of the Malyshev Polynomials, Proceedings of the 11th International Conference on Applied Informatics (Eger, Hungary, 2020). PDF (A002620, A055932)
  4. Edgar Valdebenito, Malmsten's Integral, (2019). PDF (A115252)
  5. Daniel P. Valente, The effect of topology on the dynamical behavior of oscillator networks, Ph. D. Thesis, Univ. Pennsylvalia, 2006;
  6. Guy Valette, A Classification of Spherical Curves Based on Gauss Diagrams, Arnold Math J. (2016) 2:383–405, doi:10.1007/s40598-016-0049-3.
  7. Maheswara Rao Valluri, Combinatorial Primality Test, Fiji National University (2019). Abstract There are also many other patterns of primes which are listed on the Online Encyclopedia Integer Sequence (OEIS). Readers are referred to search for any prime pattern on the OEIS.
  8. Jean Paul Van Bendegem, The Heterogeneity of Mathematical Research, a chapter in Perspectives on Interrogative Models of Inquiry, Volume 8 of the series Logic, Argumentation & Reasoning pp 73-94, Springer 2015.
  9. Daan van Berkel, On a curious property of 3435], arXiv:0911.3038 [math.HO]
  10. Marcel Van de Vel, Shuffled equi-n-squares. arXiv:1701.02325 [math.CO], 2017.
  11. Alex van den Brandhof and Paul Levrie, Tandenstokerrij, Pythagoras, Viskundetijdschrift voor Jongeren, 55ste Jaargang, Nummer 6, Juni 2016, (see the cover, pages 1, 18, 19 and the back cover).
  12. Joris van der Hoeven, Grégoire Lecerf, Sparse polynomial interpolation. Exploring fast heuristic algorithms over finite fields, Simon Fraser University (BC Canada) / Institut Polytechnique de Paris (France, 2019) hal-02382117. Abstract (A079612)
  13. W. van der Kallen, How to prove this polynomial always has integer values at all integers, arXiv preprint arXiv:1509.08811, 2015
  14. P. H. van der Kamp, doi:10.1007/s10208-009-9041-9, Global classification of two-component approximately integrable evolution equations, Found. Comput. Math 9 (5) (2009) 559-597
  15. van der Kamp, Peter H., Growth of degrees of integrable mappings. J. Difference Equ. Appl. 18 (2012), no. 3, 447-460.
  16. Peter H. van der Kamp, Somos-4 and Somos-5 are arithmetic divisibility sequences, preprint arXiv:1505.00194 (A249020, A006720, A006721)
  17. van Fossen Conrad, Eric; Flajolet, Philippe, The Fermat cubic, elliptic functions, continued fractions and a combinatorial excursion. Sém. Lothar. Combin. 54 (2005/06), Art. B54g, 44 pp.
  18. Alfred J. van der Poorten, "Elliptic Curves and Continued Fractions", J. Integer Sequences, Volume 8, 2005, Article 05.2.5.
  19. Alfred J. van der Poorten. Hyperelliptic curves, continued fractions and Somos sequences. IMS Lecture Notes 48 (2006) 212-224 doi:10.1214/074921706000000239
  20. van der Poorten, Alfred J.; Swart, Christine S. Recurrence relations for elliptic sequences: every Somos 4 is a Somos k. Bull. London Math. Soc. 38 (2006), no. 4, 546-554.
  21. Hans van Ditmarsch, Malvin Gattinger, Ioannis Kokkinis, Louwe B. Kuijer, Reachability of Five Gossip Protocols, Reachability Problems, 13th Int'l Conf. (Brussels, Belgium, RP 2019), Lecture Notes in Computer Science (LNCS Vol. 11674), Springer, Cham, 218-231. doi:10.1007/978-3-030-30806-3_17 (A307085, A318154)
  22. Aernout van Enter, Henna Koivusalo, Jacek Miękisz, Sturmian ground states in classical lattice-gas models, arXiv:1906.12103 [math-ph], 2019. JM thanks Karol Penson for introducing to him a wonderful world of the On-Line Encyclopedia of Integer Sequences...
  23. Marijke van Gans, Topics in trivalent graphs, PhD Thesis (2007)
  24. Maran van Heesch, The multiplicative complexity of symmetric functions over a field with characteristic p, Thesis, 2014;
  25. Mark van Hoeij, Erdal Imamoglu, Computing Hypergeometric Solutions of Second Order Linear Differential Equations using Quotients of Formal Solutions, preprint
  26. Mark van Hoeij, VJ Kunwar, Classifying (near)-Belyi maps with Five Exceptional Points, arXiv preprint arXiv:1604.08158, 2016. Also in Indagationes Mathematicae (2019) Vol. 30, No. 1, 136-156. doi:10.1016/j.indag.2018.09.003 (A112948) We tested this on numerous differential equations obtained from the (the Online Encyclopedia of Integer Sequences).
  27. Matty van-Son, Palindromic sequences of the Markov spectrum, arXiv:1804.10802 [math.NT], 2018. (A003602)
  28. Matty van Son, Uniqueness conjectures for extended Markov numbers, arXiv:1911.00746 [math.NT], 2019. (A022095)
  29. J. N. van Rijn, F. W. Takes, J. K. Vis, Computing and Predicting Winning Hands in the Trick-Taking Game of Klaverjas, 30th Benelux Conference on Artificial Intelligence (BNAIC 2018), 's-Hertogenbosch, the Netherlands. PDF, 2018. (A001496)
  30. S. H. M. van Zwam, Course Notes for MAT377 - Combinatorial Mathematics, Princeton University, Fall, 2012, see Section 2.8;
  31. Amalia Vanacore, Yariv N. Marmor, Emil Bashkansky, Some Metrological Aspects of Preferences Expressed by Prioritization of Alternatives, Measurement (2019) Vol. 135, 520-526. doi:10.1016/j.measurement.2018.11.012
  32. Stijn Vandamme, On the derivatives of the powers of trigonometric and hyperbolic sine and cosine, arXiv:1911.01386 [math.GM], 2019. (A133341)
  33. K. A. Van'kov, V. M. Zhuravlyov, Regular tilings and generating functions, Mat. Pros. Ser. 3, issue 22, 2018 (127–157) [in Russian].
  34. Kirill Vankov, Valerii Zhuravlev, Regular and semiregular (uniform) tilings and generating functions, hal-02535947, [math.CO], 2020. Abstract (A001169, A059716, A238823)
  35. Ilan Vardi, The error term in Golomb's sequence, Journal of Number Theory, Volume 40, Issue 1, January 1992, Pages 1-11.
  36. Jorge Garza Vargas, The Traffic Distribution of the Squared Unimodular Random Matrix and a Formula for the Moments of its ESD, Reports on Mathematical Physics (2018), Vol. 81, Issue 3, 273-282. doi:10.1016/S0034-4877(18)30044-2, also arXiv:1709.01498 [math.PR].
  37. V. K. Varma and H. Monien, Renormalization of two-body interactions due to higher-body interactions of lattice bosons, arXiv preprint arXiv:1211.5664, 2012
  38. VK Varma, S Pilati, VE Kravtsov, Conduction in quasi-periodic and quasi-random lattices: Fibonacci, Riemann, and Anderson models, arXiv preprint arXiv:1607.06276, 2016
  39. Vasic, Bane; Milenkovic, Olgica, Combinatorial constructions of low-density parity-check codes for iterative decoding. IEEE Trans. Inform. Theory 50 (2004), no. 6, 1156-1176.
  40. Vasilis, Jonatan The ring lemma in three dimensions. Geom. Dedicata 152 (2011), 51-62.
  41. Mladen Vassilev-Missana, Goldbach's n-perfect numbers as a key for proving the Goldbach's Conjecture, Notes on Number Theory and Discrete Mathematics (2005) Vol. 11, No. 1, 20-22. PDF (A071681)
  42. Jon E. Vatne, The sequence of middle divisors is unbounded, arXiv preprint arXiv:1607.02122, 2016
  43. Vincent Vatter, Enumeration schemes for restricted permutations (2005), arXiv:math/0510044, doi:10.1017/S0963548307008516, Comb. Prob. Comput. 17 (01) (2008) 137-159
  44. Vatter, Vincent Small permutation classes. Proc. Lond. Math. Soc. (3) 103 (2011), no. 5, 879-921.
  45. V. Vatter, An Erdos-Hajnal analogue for permutation classes, arXiv preprint arXiv:1511.01076, 2015
  46. Vincent Vatter, Permutation classes, arXiv:1409.5159
  47. Eduard Vatutin, Alexey Belyshev, Stepan Kochemazov, Oleg Zaikin, Natalia Nikitina, Enumeration of Isotopy Classes of Diagonal Latin Squares of Small Order Using Volunteer Computing, Russian Supercomputing Days / Суперкомпьютерные дни в России (2018). PDF (A040082, A287764)
  48. Eduard I. Vatutin, Stepan E. Kochemazov, Oleg S. Zaikin, doi:10.1007/978-3-319-67035-5_9 Applying Volunteer and Parallel Computing for Enumerating Diagonal Latin Squares of Order 9. In: Sokolinsky L., Zymbler M. (eds), Parallel Computational Technologies. PCT 2017. Communications in Computer and Information Science, vol. 753, Springer, Cham. pp. 114-129.
  49. Eduard I. Vatutin, Stepan E. Kochemazov, Oleq S.Zaikin, Maxim O. Manzuk, Natalia N. Nikitina, Vitaly S. Titov, Central symmetry properties for diagonal Latin squares, Problems of Information Technology (2019) No. 2, 3–8. doi:10.25045/jpit.v10.i2.01 (A274171, A274806, A287644, A287645, A287647, A287648, A287649, A287650, A287651, A287695, A292516, A292517, A296060, A296061)
  50. Eduard I. Vatutin, V. S. Titov, O. S. Zaikin, S. E. Kochemazov, S. U. Valyaev, A. D. Zhuravlev, M. O. Manzuk, Using grid systems for enumerating combinatorial objects with example of diagonal Latin squares, Information technologies and mathematical modeling of systems (2016), pp. 154-157. (in Russian)
  51. Vatutin E.I., Zaikin O.S., Zhuravlev A.D., Manzyuk M.O., Kochemazov S.E., Titov V.S., Using grid systems for enumerating combinatorial objects on example of diagonal Latin squares. CEUR Workshop proceedings. Selected Papers of the 7th International Conference Distributed Computing and Grid-technologies in Science and Education. 2017. Vol. 1787. pp. 486-490. urn:nbn:de:0074-1787-5.
  52. N. Vaughan, Swapping algorithm and meta-heuristic solutions for combinatorial optimization n-queens problem, in: Science and Information Conference (SAI), 2015 28-30 July 2015 Pages: 102 - 104 INSPEC Accession Number: 15420003 Conference Location : London doi:10.1109/SAI.2015.7237132
  53. Rafael Vazquez, M Krstic, Boundary control of a singular reaction-diffusion equation on a disk, arXiv preprint arXiv:1601.02010, 2016.
  54. Mark Velednitsky, New Algorithms for Three Combinatorial Optimization Problems on Graphs, Ph. D. Dissertation, University of California, Berkeley (2020). PDF (A000088)
  55. Andrea Velenich, Claudio Chamon, Leticia F. Cugliandolo and Dirk Kreimer, On the Brownian gas: a field theory with a Poissonian ground state (2008); arXiv:0802.3212
  56. Alan Veliz-Cuba, Reinhard Laubenbacher, Dynamics of semilattice networks with strongly connected dependency graph, Automatica (2019) Vol. 99, 167-174. doi:10.1016/j.automatica.2018.10.031 (A055512)
  57. Vella, Antoine, Pattern avoidance in permutations: linear and cyclic orders. Permutation patterns (Otago, 2003). Electron. J. Combin. 9 (2002/03), no. 2, Research paper 18, 43 pp.
  58. P Vellucci, AM Bersani, The class of Lucas-Lehmer polynomials, arXiv preprint arXiv:1603.01989, 2016
  59. Pierluigi Vellucci, AM Bersani, New formulas for pi involving infinite nested square roots and Gray code, arXiv preprint arXiv:1606.09597, 2016 (The OEIS is cited in version 1, but has been dropped from version 4.)
  60. Vasiliki Velona, Encoding and avoiding 2-connected patterns in polygon dissections and outerplanar graphs, arXiv:1802.03719 [math.CO], 2018. (A046736)
  61. Leandro Vendramin, Mini-couse on GAP – Exercises, Universidad de Buenos Aires (Argentina, 2020). PDF (A006720, A007542, A103379)
  62. B. J. Venkatachala, A curious bijection on natural numbers, JIS 12 (2009) 09.8.1
  63. Venturina, Randy, Nikhil Gupta, Franco Iacomella, The Decenternet Initiative, 2018. PDF (A000079, A001787, A001788, A001789, A091159)
  64. Linas Vepstas, On the Beta Transformation, 2018. PDF (A000045, A000073, A000078, A000930, A001037, A001591, A003269, A058265, A060006, A060945, A060961, A072223, A075778, A079971, A079975, A079976, A086088, A086106, A088559, A092526, A103814, A109134, A192918, A263719, A293506)
  65. A. Vera-López, M. A. Carcia-Sánchez, O. Basova, F. J. Vera-López, doi:10.1016/j.disc.2014.05.017, A generalization of Catalan numbers, Discr. Math. 332 (2014) 23-39
  66. T. Verhoeff, "Rectangular and Trapezoidal Arrangements", J. Integer Sequences, Volume 2, 1999, Article 99.1.6.
  67. Mats Vermeeren, A dynamical solution to the Basel problem, arXiv preprint arXiv:1506.05288, 2015
  68. H. A. Verrill, Sums of squares of binomial coefficients, with applications to Picard-Fuchs equations, arXiv:math/0407327
  69. F. Verstraete, J.I. Cirac, Matrix product states represent ground states faithfully (2005), arXiv:cond-mat/0505140.
  70. Jetro Vesti, Rich square-free words, arXiv:1603.01058 [math.CO], 2016.
  71. Samuel Alexandre Vidal, An Optimal Algorithm to Generate Pointed Trivalent Diagrams and Pointed Triangular Maps (2007), arXiv:0706.0969 and doi:10.1016/j.tcs.2010.04.026 Theor. Comp. Sci. 411 (2010) 2945-2967.
  72. S Vidhyalakshmi, V Krithika, K Agalya, On The Negative Pell Equation, International Journal of Emerging Technologies in Engineering Research (IJETER), Volume 4, Issue 2, February (2016),
  73. R. Vidunas, MacMahon's master theorem and totally mixed Nash equilibria, arXiv preprint arXiv:1401.5400, 2014
  74. M. Vielhaber, On the linear complexity of multisequences, bijections between Zahlen and Number tuples, and partitions, in Applied Algebra and Number Theory, edited by Gerhard Larcher, et al., Cambridge Univ. Press, 2014.
  75. M. Vielhaber and M. del Pilar Canales Chacon, The Linear Complexity Deviation of Multisequences: Formulae for Finite Lengths and Asymptotic Distributions, in T. Hellesth and J. Jedwab, eds., SETA 2012, LNCS 7280, 2012, pp. 168-180.
  76. A. Vieru, Agoh's conjecture: its proof, its generalizations, its analogues, arXiv:1107.2938, 2011.
  77. Andrei Vieru, Euler constant as a renormalized value of Riemann zeta function at its pole. Rationals related to Dirichlet L-functions, preprint arXiv:1306.0496 (A008836, A112932)
  78. Andrei Vieru, Analytic renormalization of multiple zeta functions. Geometry and combinatorics of generalized Euler reflection formula for MZV, arXiv preprint arXiv:1601.04703, 2016.
  79. C. Vignat and T. Wakhare, Finite generating functions for the sum of digits sequence, arXiv:1708.06479 [math.NT], 2017.
  80. Vignat, C. & Wakhare, T., Settling some sum suppositions, Acta Math. Hungar. (2018).
  81. Erik Vigren, Andreas Dieckmann, Simple Solutions of Lattice Sums for Electric Fields Due to Infinitely Many Parallel Line Charges, Symmetry (2020) Vol. 12, No. 6, 1040. doi:10.3390/sym12061040 (A104203)
  82. Sujith Vijay, On large primitive subsets of {1, 2, ..., 2n}, arXiv:1804.01740 [math.CO], 2018. (A174094)
  83. A .Vijayasankar, M. A. Gopalan, V. Krithika, On The Negative Pell Equation y2 = 112x2 - 7, International Journal of Engineering and Applied Sciences (IJEAS), Volume 4, Issue 7, July 2017. (A031396, A031398, A130226)
  84. Antre Rishikesh Vilas, A. Cendil Kumar, Goli Divakar, Andhale Ganesh Sakharam and Jomon Joseph, Structure, Shape, Ms Spectral Data and Biological Activities of Fullerenes;
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  86. Andrew Vince, The average size of a connected vertex set of a graph-explicit formulas and open problems, University of Florida (2019). PDF (A000129, A001333)
  87. Andrew Vince and Miklos Bona, The Number of Ways to Assemble a Graph, Arxiv preprint arXiv:1204.3842, 2012
  88. Le Anh Vinh, "On Fibonacci-Like Sequences", J. Integer Sequences, Volume 10, 2007, Article 07.10.2.
  89. A. Viola, Analysis of Hashing Algorithms and a New Mathematical Transform
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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.
  • 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.