A215117 G.f. A(x) satisfies: A(A(A(A(x)))) = G(x) where G(x) = x + 3*x^2 + x*G(G(G(G(x)))) is the g.f. of A215116.

1, 1, 1, 49, 721, 17281, 452065, 13511953, 443435185, 15816390241, 606861668161, 24867738772849, 1082158542264721, 49785517156216897, 2412544311495241633, 122762020478952148177, 6542028190536528941425, 364254737003651267997985, 21146448814786605196994305

Offset

1,4

Links

Table of n, a(n) for n=1..19.

Formula

a(n) == 1 (mod 48).

Example

G.f.: A(x) = x + x^2 + x^3 + 49*x^4 + 721*x^5 + 17281*x^6 + 452065*x^7 +...
Let G(x) = A(A(A(A(x)))):
G(x) = x + 4*x^2 + 16*x^3 + 256*x^4 + 4864*x^5 + 111616*x^6 + 2983936*x^7 +...
such that G(x) = x + 3*x^2 + x*G(G(G(G(x)))):
G(G(G(G(x)))) = x + 16*x^2 + 256*x^3 + 4864*x^4 + 111616*x^5 + 2983936*x^6 +...

Prog

(PARI) {a(n)=local(A=x+x^2, B=x+4*x^2); for(i=1, n+1, B=x+3*x^2+x*subst(B, x, subst(B, x, subst(B, x, B+x^2*O(x^n)))));
for(j=1, n+1, A=round((3*A+subst(B, x, serreverse(subst(A, x, subst(A, x, A+x^2*O(x^n))))))/4));; polcoeff(A, n)}
for(n=1, 31, print1(a(n), ", "))

Crossrefs

Cf. A215116, A213009, A215115, A215119.

Sequence in context: A166832 A299711 A175775 * A350982 A289992 A357653

Adjacent sequences: A215114 A215115 A215116 * A215118 A215119 A215120

Keyword

nonn

Author

Paul D. Hanna, Aug 03 2012

Status

approved