A217526 From the enumeration of involutions avoiding the pattern 4321.

0, 0, 0, 0, 0, 2, 6, 18, 47, 123, 318, 830, 2182, 5792, 15504, 41828, 113626, 310564, 853458, 2356770, 6536372, 18199274, 50852008, 142547548, 400763211, 1129760403, 3192727784, 9043402488, 25669818462, 73007772788, 208023278194, 593742784814, 1697385471195

Offset

0,6

Links

Alois P. Heinz, Table of n, a(n) for n = 0..650

Piera Manara and Claudio Perelli Cippo, The fine structure of 4321 avoiding involutions and 321 avoiding involutions, PU. M. A. Vol. 22 (2011), 227-238. See page 233.

Formula

Manara and Perelli Cippo give a g.f.:

G.f.: (1 - x - sqrt(1 - 2*x - 3*x^2))/2 - x^2/((1 - x)*(1 - x^2)).

Recurrence (for n>5): (n-5)*n*(2*n-7)*a(n) = 2*(n-3)*(2*n^2 - 12*n + 15)*a(n-1) + 2*(4*n^3 - 47*n^2 + 177*n - 215)*a(n-2) - 2*(n-4)*(2*n^2 - 6*n - 5)*a(n-3) - 3*(n-5)*(n-4)*(2*n-5)*a(n-4). - Vaclav Kotesovec, Aug 18 2013

a(n) ~ 3^n/(2*sqrt(3*Pi)*n^(3/2)). - Vaclav Kotesovec, Aug 18 2013

Prog

(PARI) all_a(m) = { x = y+O(y^(m+1)); P = (1 - x - sqrt(1-2*x-3*x^2))/2 - x^2/((1-x)*(1-x^2)); for (n=0, m, print1(polcoeff(P, n, y), ", ")); } \\ Michel Marcus, Feb 08 2013

Crossrefs

Sequence in context: A072827 A248169 A002529 * A018027 A218759 A295499

Adjacent sequences: A217523 A217524 A217525 * A217527 A217528 A217529

Keyword

nonn

Author

N. J. A. Sloane, Oct 13 2012

Extensions

More terms from Michel Marcus, Feb 08 2013

Status

approved