OFFSET
1,14
COMMENTS
Euler transform of period 45 sequence [1, -1, 0, 1, 0, 0, -1, -1, -1, 0, 1, 0, -1, 1, 0, 1, -1, 1, 1, 0, 0, -1, -1, 0, 0, 1, 1, -1, 1, 0, 1, -1, 0, 1, 0, -1, -1, -1, 0, 0, 1, 0, -1, 1, 0,...].
FORMULA
G.f. A(x) satisfies 0=f(A(x),A(x^2)) where f(u,v) = u^2 - v + u*v^3 + u^3*v^2 - 2*u*v*(1 - u + v + u*v).
G.f. A(x) satisfies 0 = f(A(x), A(x^2), A(x^4)) where f(u, v, w) = w + 2*u*w + 2*u*v*w - u*w^2 - u^2*v -u*v^2*w. - Michael Somos, Dec 11 2008
EXAMPLE
q + q^2 + q^5 + q^6 - q^8 - q^9 - q^10 - q^11 - 2*q^14 - q^15 + 2*q^16 + ...
PROG
(PARI) {a(n)=if(n<1, 0, n--; polcoeff( prod(k=1, n, (1-x^k+x*O(x^n))^-(kronecker(5, k\9-k%9)*if(k%9==0, -1, k%3>0))), n))}
(PARI) {a(n)=local(A, u, v); if(n<0, 0, A=x; for(k=2, n, u=A+x*O(x^k); v=subst(u, x, x^2); A-=x^k*polcoeff(u^2-v+u*v^3+u^3*v^2-2*u*v*(1-u+v+u*v), k+1)/2); polcoeff(A, n))}
CROSSREFS
KEYWORD
sign
AUTHOR
Michael Somos, Mar 09 2004, Dec 11 2008
STATUS
approved