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

Author

Jay Pantone, Sep 03 2013

Keywords

• nonn

Examples

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

Links

• 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