A054274 Expansion of g.f. Product_{n>=1} (1-x^n)*(1-x^(5*n))/(1-x^(3*n))^2.

1, -1, -1, 2, -2, -2, 6, -3, -5, 12, -8, -9, 24, -14, -18, 42, -26, -31, 76, -45, -54, 126, -76, -88, 210, -121, -144, 332, -196, -225, 526, -302, -351, 804, -464, -531, 1224, -698, -800, 1818, -1040, -1179, 2688, -1519, -1728, 3902, -2212, -2491, 5632, -3167, -3571, 8016, -4508

Offset

0,4

Links

G. C. Greubel, Table of n, a(n) for n = 0..1000

A. J. Guttmann, Indicators of solvability for lattice models, Discrete Math., 217 (2000), 167-189.

Formula

Euler transform of period 15 sequence [ -1, -1, 1, -1, -2, 1, -1, -1, 1, -2, -1, 1, -1, -1, 0, ...]. - Michael Somos, Sep 21 2005

Expansion of eta(q)*eta(q^5)/eta(q^3)^2 in powers of q. - Michael Somos, Sep 21 2005

Example

G.f. = 1 - q - q^2 + 2*q^3 - 2*q^4 - 2*q^5 + 6*q^6 - 3*q^7 - 5*q^8 + 12*q^9 + ...

Mathematica

QP = QPochhammer; s = QP[q]*(QP[q^5]/QP[q^3]^2) + O[q]^60; CoefficientList[ s, q] (* Jean-François Alcover, Nov 30 2015, adapted from PARI *)

Prog

(PARI) {a(n)=local(A); if(n<0, 0, A=x*O(x^n); polcoeff( eta(x+A)* eta(x^5+A)/eta(x^3+A)^2, n))} /* Michael Somos, Sep 21 2005 */
(Magma) m:=60; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!( (&*[(1-x^j)*(1-x^(5*j))/(1-x^(3*j))^2: j in [1..m+2]]) )); // G. C. Greubel, Jul 31 2019

Crossrefs

Sequence in context: A081668 A126615 A158524 * A053695 A210550 A208659

Adjacent sequences: A054271 A054272 A054273 * A054275 A054276 A054277

Keyword

sign

Author

N. J. A. Sloane, May 08 2000

Status

approved