A116703 Number of permutations of length n which avoid the patterns 231, 4123.
1, 2, 5, 13, 33, 82, 202, 497, 1224, 3017, 7439, 18343, 45228, 111514, 274945, 677894, 1671393, 4120937, 10160465, 25051354, 61765902, 152288233, 375477484, 925766477, 2282543187, 5627772815, 13875674756, 34211464510, 84350802705
Offset: 1
Links
- G. C. Greubel, Table of n, a(n) for n = 1..1000
- A. M. Baxter, L. K. Pudwell, Ascent sequences avoiding pairs of patterns, The Electronic Journal of Combinatorics, Volume 22, Issue 1 (2015) Paper #P1.58.
- Christian Bean, Bjarki Gudmundsson, Henning Ulfarsson, Automatic discovery of structural rules of permutation classes, arXiv:1705.04109 [math.CO], 2017.
- David Callan, Toufik Mansour, Enumeration of small Wilf classes avoiding 1342 and two other 4-letter patterns, Pure Mathematics and Applications (2018) Vol. 27, No. 1, 62-97.
- Toufik Mansour and Mark Shattuck, Avoidance of type (1,2) patterns by Catalan words, Turkish Journal of Analysis and Number Theory, May 2017. See item 1-23 in Table 1, p. 3.
- Lara Pudwell, Systematic Studies in Pattern Avoidance, 2005.
- L. Pudwell, Pattern-avoiding ascent sequences, Slides from a talk, 2015.
- L. Pudwell, A. Baxter, Ascent sequences avoiding pairs of patterns, Slides, Permutation Patterns 2014, East Tennessee State University Jul 07 2014.
- Index entries for linear recurrences with constant coefficients, signature (4,-5,3).
Crossrefs
Cf. A000930.
Programs
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Mathematica
CoefficientList[Series[x*(1-2*x+2*x^2)/(1-4*x+5*x^2-3*x^3), {x, 0, 50}], x] (* G. C. Greubel, Apr 29 2017 *) -
PARI
x='x+O('x^50); Vec(x*(1-2*x+2*x^2)/(1-4*x+5*x^2-3*x^3)) \\ G. C. Greubel, Apr 29 2017
Formula
G.f.: -((2x^2-2x+1)x)/(3x^3-5x^2+4x-1).
Binomial transform of A000930 starting with offset 1: [1, 1, 2, 3, 4, 6, 9, ...]. - Gary W. Adamson, Oct 23 2007
Extensions
Edited by N. J. A. Sloane, Mar 16 2008
Comments