OFFSET
0,3
COMMENTS
Compare to the identity: Sum_{n=-oo..+oo} x^n * (1 - x^n)^n = 0.
LINKS
Paul D. Hanna, Table of n, a(n) for n = 0..2200
FORMULA
G.f.: Sum_{n=-oo..+oo} (-1)^n * x^(3*n^2-n) / (1 - x^n)^(3*n).
For n>0, a(n) = 1 iff n = 3^k for k>=0 (conjecture).
EXAMPLE
G.f.: A(x) = 1 + x - 3*x^2 + x^3 - 12*x^4 - 9*x^5 - 8*x^6 - 20*x^7 - 59*x^8 + x^9 - 43*x^10 - 54*x^11 - 101*x^12 - 77*x^13 - 89*x^14 + 127*x^15 +...
PROG
(PARI) {a(n) = local(A=1); A = sum(k=-n-1, n+1, x^k*(1-x^k + x*O(x^n) )^(3*k) ); polcoeff(A, n)}
for(n=0, 60, print1(a(n), ", "))
CROSSREFS
KEYWORD
sign
AUTHOR
Paul D. Hanna, Mar 29 2016
STATUS
approved