A284715 Number of indecomposable permutations avoiding the pattern 3214.

1, 1, 3, 13, 65, 351, 1999, 11872, 73023, 462889, 3012162, 20056509, 136274564, 942624033, 6624531216, 47219125251, 340867497305, 2488891555146, 18361241675953, 136728796412286, 1026878910257061, 7772561249596928, 59253932922240432, 454708539839137050

Offset

1,3

Links

Vincenzo Librandi, Table of n, a(n) for n = 1..200

A. L. L. Gao, S. Kitaev, P. B. Zhang. On pattern avoiding indecomposable permutations, arXiv:1605.05490 [math.CO], 2016.

Formula

a(n) ~ 3^(2*n+7/2) * phi^2 / (16*Pi*n^4), where phi = A001622 = (1+sqrt(5))/2 is the golden ratio. - Vaclav Kotesovec, Apr 02 2017

Mathematica

Rest[CoefficientList[Series[1/2*(Sqrt[1-4*x] + 1)*((1 + 5*x - (1-9*x)^(3/4) * (1-x)^(1/4) * HypergeometricPFQ[{-1/4, 3/4}, {1}, 64*x/((x-1)*(1-9*x)^3)])/(6*x^2) - 1), {x, 0, 30}], x]] (* Vaclav Kotesovec, Apr 02 2017 *)

Crossrefs

Sequence in context: A352706 A368973 A256332 * A364473 A186577 A141342

Adjacent sequences: A284712 A284713 A284714 * A284716 A284717 A284718

Keyword

nonn

Author

N. J. A. Sloane, Apr 02 2017

Extensions

More terms from Vaclav Kotesovec, Apr 02 2017

Status

approved