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 A054274 Expansion of g.f. Product_{n>=1} (1-x^n)*(1-x^(5*n))/(1-x^(3*n))^2. 1
 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 (list; graph; refs; listen; history; text; internal format)
 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:=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

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Last modified December 4 06:57 EST 2023. Contains 367557 sequences. (Running on oeis4.)