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
KEYWORD
nonn
AUTHOR
N. J. A. Sloane, Oct 13 2012
EXTENSIONS
More terms from Michel Marcus, Feb 08 2013
STATUS
approved