A217925 G.f. A(x) satisfies A(x) = 1 + x*A(x)*A(x^2)^2.

1, 1, 1, 3, 5, 10, 19, 40, 77, 155, 306, 610, 1207, 2400, 4760, 9456, 18765, 37257, 73955, 146813, 291434, 578524, 1148434, 2279720, 4525487, 8983421, 17832976, 35399824, 70271944, 139495472, 276910976, 549691232, 1091185133, 2166094309, 4299884233, 8535634803, 16943967775

Offset: 0

Author

Joerg Arndt, Oct 15 2012

Keywords

• nonn

Comments

What does this sequence count?

Links

• Vaclav Kotesovec, Table of n, a(n) for n = 0..1000

Crossrefs

Cf. A000108 (A(x) = 1 + x*A(x)^2), A000621 (A(x) = 1 + x*A(x)*A(x^2)).

Cf. A036675 (A(x) = 1 + x*A(x)^2*A(x^2)), A101913 (A(x) = 1 + x*A(x)*A(x^3); for abs. values).

Programs

Maxima

T(n,m):=if n=m then 1 else sum(binomial(m+k-1,k)*T((n-m)/2,2*k),k,1,(n-m)/4);
makelist(T(4*n+1,1),n,0,25); /* Vladimir Kruchinin, Mar 25 2015 */

PARI

N=66;  R=O('x^N);  x='x+R;
F = 1 + x;
{ for (k=1,N+1, F = 1 + x * F * subst(F,'x,'x^2)^2 + R; ); }
Vec(F+O('x^N))

Formula

a(n) ~ c * d^n, where d = 1.985085392419660786124534041173530134614822710253953085885966352..., c = 0.322822740100478716884116064042886830242825005622702339543369128... . - Vaclav Kotesovec, Aug 10 2014

a(n) = T(4*n+1,1), where T(n,m) = Sum_{k=1..(n-m)/4} C(m+k-1,k)*T((n-m)/2,2*k). - Vladimir Kruchinin, Mar 25 2015