A226434 The number of sum decomposable permutations which avoid the patterns 3124 and 4312.

0, 1, 3, 10, 37, 146, 595, 2456, 10167, 42027, 173201, 711397, 2912633, 11891030, 48425597, 196790382, 798251109, 3232928429, 13075849791, 52825304031, 213196622183, 859690304703, 3463979709111, 13948292729231, 56132430446203, 225778880966297, 907726113188331, 3647961305524521, 14655086058873287, 58855311286307572

Offset

1,3

Links

Table of n, a(n) for n=1..30.

Jay Pantone, The Enumeration of Permutations Avoiding 3124 and 4312, arXiv:1309.0832 [math.CO], (2013)

Formula

G.f.: -(8*x^5 - 16*x^4 + 19*x^3 - 8*x^2 - sqrt(-4*x + 1)*(2*x^4 + x^3 - 4*x^2 + x) + x)/(12*x^4 - 31*x^3 + 27*x^2 + sqrt(-4*x + 1)*(4*x^4 - 13*x^3 + 15*x^2 - 7*x + 1) - 9*x + 1)

Conjecture: +(95*n+537)*(n+2)*a(n) +(95*n^2-16421*n-14748) *a(n-1) +(-6403*n^2+124495*n-60066) *a(n-2) +(21565*n^2-354883*n+596496) *a(n-3) +2*(-5092*n^2+138877*n-395970) *a(n-4) +8*(-2470*n^2+11113*n+12744) *a(n-5) +192*(38*n-67)*(2*n-13)*a(n-6)=0. - R. J. Mathar, Jun 14 2016

Example

Example: a(4)=10 because there are 10 sum decomposable permutations of length 4 which avoid the patterns 3124 and 4312.

Crossrefs

Sequence in context: A052893 A052818 A299501 * A151055 A151056 A109081

Adjacent sequences: A226431 A226432 A226433 * A226435 A226436 A226437

Keyword

nonn

Author

Jay Pantone, Sep 03 2013

Status

approved