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A092872 Expansion of r(q^9) / (r(q) r(q^3)) in powers of q where r() is the Rogers-Ramanujan continued fraction function (A007325). 0
1, 1, 0, 0, 1, 1, 0, -1, -1, -1, -1, 0, 0, -2, -1, 2, 3, 0, -1, 2, 3, 0, -1, -1, -2, -2, 0, 0, -4, -3, 5, 7, 0, -2, 4, 6, 0, -4, -3, -5, -6, 0, 0, -8, -6, 10, 14, 0, -5, 9, 13, 0, -7, -5, -9, -10, 0, 0, -16, -12, 20, 28, 0, -8, 17, 24, 0, -14, -11, -18, -20, 0, 0, -30, -21, 36, 50, 0, -16, 30, 44, 0, -23, -18, -31, -34, 0, 0, -52, -38, 63 (list; graph; refs; listen; history; text; internal format)
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,...].

LINKS

Table of n, a(n) for n=1..91.

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

Sequence in context: A129391 A129390 A123590 * A141455 A292627 A113125

Adjacent sequences:  A092869 A092870 A092871 * A092873 A092874 A092875

KEYWORD

sign

AUTHOR

Michael Somos, Mar 09 2004, Dec 11 2008

STATUS

approved

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Last modified May 14 19:53 EDT 2021. Contains 343903 sequences. (Running on oeis4.)