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%I #8 Jun 14 2016 10:34:33
%S 0,1,3,10,37,146,595,2456,10167,42027,173201,711397,2912633,11891030,
%T 48425597,196790382,798251109,3232928429,13075849791,52825304031,
%U 213196622183,859690304703,3463979709111,13948292729231,56132430446203,225778880966297,907726113188331,3647961305524521,14655086058873287,58855311286307572
%N The number of sum decomposable permutations which avoid the patterns 3124 and 4312.
%H Jay Pantone, <a href="http://arxiv.org/abs/1309.0832">The Enumeration of Permutations Avoiding 3124 and 4312</a>, arXiv:1309.0832 [math.CO], (2013)
%F 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)
%F 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
%e Example: a(4)=10 because there are 10 sum decomposable permutations of length 4 which avoid the patterns 3124 and 4312.
%K nonn
%O 1,3
%A _Jay Pantone_, Sep 03 2013
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