OFFSET
0,5
LINKS
INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 656
FORMULA
G.f.: RootOf(-_Z+_Z^2+_Z^3+x)-RootOf(-_Z+_Z^2+_Z^3+x)^2-x
Recurrence: {a(1)=0, a(2)=0, a(3)=1, a(4)=3, (30-135*n+135*n^2)*a(n)+(-130-107*n+29*n^2)*a(n+1)+(-281*n-198-91*n^2)*a(n+2)+(15*n^2+75*n+90)*a(n+3)}
From Seiichi Manyama, Nov 22 2024: (Start)
G.f.: (x*B(x))^3 where B(x) is the g.f. of A001002.
a(n) = 3 * Sum_{k=0..n-3} binomial(n+k,k) * binomial(k,n-3-k)/(n+k). (End)
a(n) ~ 3^(3*n - 5/2) / (sqrt(Pi) * 2^(3/2) * n^(3/2) * 5^(n - 1/2)). - Vaclav Kotesovec, Nov 22 2024
MAPLE
spec := [S, {C=Prod(B, B), B=Union(S, C, Z), S=Prod(B, C)}, unlabeled]: seq(combstruct[count](spec, size=n), n=0..20);
PROG
(PARI) my(N=30, x='x+O('x^N)); concat([0, 0, 0], Vec(serreverse(x-x^2-x^3)-serreverse(x-x^2-x^3)^2-x)) \\ Seiichi Manyama, Nov 22 2024
(PARI) a(n) = 3*sum(k=0, n-3, binomial(n+k, k)*binomial(k, n-3-k)/(n+k)); \\ Seiichi Manyama, Nov 22 2024
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
encyclopedia(AT)pommard.inria.fr, Jan 25 2000
EXTENSIONS
More terms from Seiichi Manyama, Nov 21 2024
STATUS
approved