OFFSET
0,6
LINKS
Alois P. Heinz, Table of n, a(n) for n = 0..1000
FORMULA
Recurrence: (n+3)*a(n) = (2*n+3)*a(n-1) - n*a(n-2) + (2*n-3)*a(n-3) + (2*n-9)*a(n-5) - (n-6)*a(n-6) - (2*n-15)*a(n-7) - (n-9)*a(n-8). - Vaclav Kotesovec, Aug 25 2014
a(n) ~ c * d^n / n^(3/2), where d = 2.0423505898306085793498312456063... is the root of the equation -1 - 2*d - d^2 + d^3 - 2*d^4 + d^5 = 0, c = 1.36047848416839112694538628599558274531... . - Vaclav Kotesovec, Aug 25 2014
G.f. A(x) satisfies: A(x) = (1 + x^3 * A(x)^2) / (1 - x + x^3 + x^4). - Ilya Gutkovskiy, Jul 20 2021
MAPLE
a:= proc(n) option remember;
`if`(n=0, 1, a(n-1) +add(a(k)*a(n-3-k), k=2..n-3))
end:
seq(a(n), n=0..50); # Alois P. Heinz, May 08 2011
MATHEMATICA
Clear[ a ]; a[ 0 ]=1; a[ n_Integer ] := a[ n ]=a[ n-1 ]+Sum[ a[ k ]*a[ n-3-k ], {k, 2, n-3} ];
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
STATUS
approved