A101108 Expansion of solution to a functional equation.

1, 1, 1, 0, 1, 1, 1, -1, 0, 1, 2, 1, 0, 0, 0, 0, 0, -1, -1, 1, 4, 3, 1, -2, 1, 1, 0, -3, -3, 1, 4, 4, -1, -3, -3, 2, 0, -4, -4, 1, 11, 9, 3, -6, -1, 3, 3, -8, -10, 2, 13, 14, -3, -10, -7, 4, 0, -12, -15, 1, 25, 21, 3, -16, -5, 7, 3, -18, -26, 1, 29, 34, -5, -24, -17, 11, 5, -27, -36, 0, 58, 54, 12, -37, -12, 20, 15, -42, -63, -1

Offset

0,11

Links

Table of n, a(n) for n=0..89.

Formula

Given g.f. A(x), then B(x)=x*A(x^5) satisfies 0=f(B(x),B(x^2),B(x^4)) where f(u,v,w)=uv^4+v^3w^2+u^2w^3-u^3vw.

Prog

(PARI) a(n)=local(B, A, k); if(n<0, 0, k=(3+sqrtint(9+40*n))\10; A= sum(i=-k, k, (-1)^i*x^((5*i^2+3*i)/2), x*O(x^n)) /sum(i=-k, k, (-1)^i*x^((5*i^2+i)/2), x*O(x^n)); B=k=1; while(k<=n, k*=2; B/=A; A=subst(A, x, x^2) +x*O(x^n)); polcoeff(B, n))
(PARI) {a(n)=if(n<0, 0, polcoeff( prod(k=1, n, (1-x^k)^-sum(i=0, valuation(k, 2), kronecker(5, k/2^i)), 1+x*O(x^n)), n))}

Crossrefs

Cf. A007325.

Sequence in context: A016011 A263338 A103522 * A279280 A284093 A284095

Adjacent sequences: A101105 A101106 A101107 * A101109 A101110 A101111

Keyword

sign

Author

Michael Somos, Dec 01 2004

Status

approved