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
KEYWORD
sign
AUTHOR
N. J. A. Sloane, May 08 2000
STATUS
approved