A215115 G.f. A(x) satisfies: A(A(A(x))) = G(x) where G(x) = x + 2*x^2 + x*G(G(G(x))) is the g.f. of A215114.

1, 1, 1, 19, 163, 2269, 34093, 584767, 10989271, 224143489, 4910384809, 114714875755, 2841991084747, 74337591206629, 2045557726962949, 59036247882081847, 1782385894711138303, 56166016733387381449, 1843556640469175481985, 62915735570546535121891

Offset

1,4

Links

Table of n, a(n) for n=1..20.

Formula

a(n) == 1 (mod 18).

Example

G.f.: A(x) = x + x^2 + x^3 + 19*x^4 + 163*x^5 + 2269*x^6 + 34093*x^7 +...
Let G(x) = A(A(A(x))):
G(x) = x + 3*x^2 + 9*x^3 + 81*x^4 + 891*x^5 + 11907*x^6 + 184437*x^7 +...
such that G(x) = x + 2*x^2 + x*G(G(G(x))):
G(G(G(x))) = x + 9*x^2 + 81*x^3 + 891*x^4 + 11907*x^5 + 184437*x^6 +...

Prog

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

Crossrefs

Cf. A215114, A213009, A215117, A215119.

Sequence in context: A197500 A341398 A212850 * A142128 A158966 A038864

Adjacent sequences: A215112 A215113 A215114 * A215116 A215117 A215118

Keyword

nonn

Author

Paul D. Hanna, Aug 03 2012

Status

approved