A097089 Exponents of 2 that form the denominators of coefficients in function A(x) such that A(A(x)) = x+x^2.

0, 0, 1, 2, 2, 4, 6, 4, 8, 7, 11, 12, 13, 13, 14, 15, 18, 18, 20, 22, 23, 24, 26, 26, 25, 26, 30, 31, 33, 32, 34, 33, 38, 38, 39, 39, 42, 44, 46, 46, 46, 48, 51, 52, 53, 53, 55, 55, 56, 55, 59, 61, 62, 63, 65, 66, 68, 68, 70, 71, 73

Offset

0,4

Comments

A097088 lists the reduced numerators.

Links

Table of n, a(n) for n=0..60.

Formula

G.f.: A(x) = Sum_{n>=0} A097088(n)/2^a(n) where A(A(x)) = x + x^2.

Prog

(PARI) {a(n)=local(A, B, F=x+x^2+x*O(x^n)); A=F; if(n==0, 0, for(i=0, n, B=serreverse(A); A=(A+subst(B, x, F))/2); valuation(denominator(polcoeff(A, n, x)), 2))}

Crossrefs

Cf. A097088.

Sequence in context: A220194 A220358 A089002 * A317764 A318075 A318343

Adjacent sequences: A097086 A097087 A097088 * A097090 A097091 A097092

Keyword

nonn

Author

Paul D. Hanna, Jul 23 2004

Status

approved