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A217526 From the enumeration of involutions avoiding the pattern 4321. 1
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified October 19 16:17 EDT 2019. Contains 328223 sequences. (Running on oeis4.)