A268298 G.f.: Sum_{n=-oo..+oo} x^n * (1 - x^n)^(3*n).

1, 1, -3, 1, -12, -9, -8, -20, -59, 1, -43, -54, -101, -77, -89, 127, -307, -135, -26, -170, 73, 85, 199, -252, -888, 1066, 924, 1, 1177, -405, 2970, -464, 1009, -164, 5577, 10396, -2978, -665, 10869, -1286, 14576, -819, 15499, -902, 19934, 17551, 32546, -1080, -51905, 53089, 74231, -24309, 55317, -1377, -80, 42439, 103857, -75581, 117016, -1710

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

Cf. A260147.

Sequence in context: A046089 A113360 A089434 * A291418 A219512 A186695

Adjacent sequences: A268295 A268296 A268297 * A268299 A268300 A268301

Keyword

sign

Author

Paul D. Hanna, Mar 29 2016

Status

approved