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
Keywords
Crossrefs
Cf. A097088.
Programs
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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))}
Formula
G.f.: A(x) = Sum_{n>=0} A097088(n)/2^a(n) where A(A(x)) = x + x^2.
Comments