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A226434 The number of sum decomposable permutations which avoid the patterns 3124 and 4312. 1
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 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,3
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
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
KEYWORD
nonn
AUTHOR
Jay Pantone, Sep 03 2013
STATUS
approved

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Last modified June 16 22:16 EDT 2024. Contains 373432 sequences. (Running on oeis4.)