|
%I #49 Feb 07 2022 00:27:34
%S 1,2,5,13,33,82,202,497,1224,3017,7439,18343,45228,111514,274945,
%T 677894,1671393,4120937,10160465,25051354,61765902,152288233,
%U 375477484,925766477,2282543187,5627772815,13875674756,34211464510,84350802705
%N Number of permutations of length n which avoid the patterns 231, 4123.
%C Also number of permutations of length n which avoid the patterns 312, 2341, 3412; or avoid the patterns 132, 1324, 3214, etc.
%C Except for the offset, this is the p-INVERT of (1,1,1,1,1,...) for p(S) = 1 - S - S^3; see A291000. - _Clark Kimberling_, Aug 24 2017
%H G. C. Greubel, <a href="/A116703/b116703.txt">Table of n, a(n) for n = 1..1000</a>
%H A. M. Baxter, L. K. Pudwell, <a href="http://www.combinatorics.org/ojs/index.php/eljc/article/view/v22i1p58">Ascent sequences avoiding pairs of patterns</a>, The Electronic Journal of Combinatorics, Volume 22, Issue 1 (2015) Paper #P1.58.
%H Christian Bean, Bjarki Gudmundsson, Henning Ulfarsson, <a href="https://arxiv.org/abs/1705.04109">Automatic discovery of structural rules of permutation classes</a>, arXiv:1705.04109 [math.CO], 2017.
%H David Callan, Toufik Mansour, <a href="https://doi.org/10.1515/puma-2015-0027">Enumeration of small Wilf classes avoiding 1342 and two other 4-letter patterns</a>, Pure Mathematics and Applications (2018) Vol. 27, No. 1, 62-97.
%H Toufik Mansour and Mark Shattuck, <a href="http://pubs.sciepub.com/tjant/5/3/4/">Avoidance of type (1,2) patterns by Catalan words</a>, Turkish Journal of Analysis and Number Theory, May 2017. See item 1-23 in Table 1, p. 3.
%H Lara Pudwell, <a href="http://faculty.valpo.edu/lpudwell/maple/webbook/bookmain.html">Systematic Studies in Pattern Avoidance</a>, 2005.
%H L. Pudwell, <a href="http://faculty.valpo.edu/lpudwell/slides/ascseq.pdf">Pattern-avoiding ascent sequences</a>, Slides from a talk, 2015.
%H L. Pudwell, A. Baxter, <a href="http://faculty.valpo.edu/lpudwell/slides/pp2014_pudwell.pdf">Ascent sequences avoiding pairs of patterns</a>, Slides, Permutation Patterns 2014, East Tennessee State University Jul 07 2014.
%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (4,-5,3).
%F G.f.: -((2x^2-2x+1)x)/(3x^3-5x^2+4x-1).
%F Binomial transform of A000930 starting with offset 1: [1, 1, 2, 3, 4, 6, 9, ...]. - _Gary W. Adamson_, Oct 23 2007
%t 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 *)
%o (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
%Y Cf. A000930.
%K nonn,easy
%O 1,2
%A _Lara Pudwell_, Feb 26 2006
%E Edited by _N. J. A. Sloane_, Mar 16 2008
|
