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 A092531 Expansion of (1+x^10)/((1-x)*(1-x^4)^2*(1-x^8)). 0
 1, 1, 1, 1, 3, 3, 3, 3, 7, 7, 8, 8, 14, 14, 16, 16, 25, 25, 29, 29, 41, 41, 47, 47, 63, 63, 72, 72, 92, 92, 104, 104, 129, 129, 145, 145, 175, 175, 195, 195, 231, 231, 256, 256, 298, 298, 328, 328, 377, 377, 413, 413, 469, 469, 511, 511, 575, 575, 624, 624, 696, 696, 752, 752 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,5 LINKS G. Nebe, E. M. Rains and N. J. A. Sloane, Self-Dual Codes and Invariant Theory, Springer, Berlin, 2006. Index entries for linear recurrences with constant coefficients, signature (1,1,-1,1,-1,-1,1,1,-1,-1,1,-1,1,1,-1). FORMULA G.f.: ( 1+x^4+x^8-x^2-x^6 ) / ( (1+x^4) * (1+x^2)^2 * (1+x)^3 * (1-x)^4 ). - R. J. Mathar, Dec 18 2014 a(n) = (2*n^3 + 21*n^2 + 175*n + 441 + 3*(n^2 + 7*n + 29)*(-1)^n + 30*(2*n + 7)*(-1)^((2*n - 1 + (-1)^n)/4) + 30*(-1)^((6*n - 1 + (-1)^n)/4) + 48*((-1)^((2*n - 3 + (-1)^n + 2*(-1)^((2*n - 1 + (-1)^n)/4))/8) - (-1)^((6*n - 5 + 3*(-1)^n + 2*(-1)^((2*n - 1 + (-1)^n)/4))/8)))/768. - Luce ETIENNE, Mar 31 2015 Shorter version of above: a(n) = (2*n^3 + 21*n^2 + 175*n + 441 + 3*(n^2 + 7*n + 29)*(-1)^n + 30*(2*n + 7)*sign(1-n%4+n%2) + 30*sign(2-(n+1)%4-n%2) + 48*((5*n-n^2)%4)*sign(5-n%8))/768, where sign(x) = x/abs(x), and a%b = a (mod b). - Derek Orr, Apr 05 2015 MATHEMATICA CoefficientList[Series[(1 + x^4 + x^8 - x^2 - x^6) / ((x^4 + 1) (1 + x^2)^2 (1 + x)^3 (x-1)^4), {x, 0, 70}], x] (* Vincenzo Librandi, Apr 05 2015 *) PROG (PARI) Vec((1+x^10)/((1-x)*(1-x^4)^2*(1-x^8)) + O(x^80)) \\ Michel Marcus, Apr 05 2015 (PARI) a(n) = (2*n^3 + 21*n^2 + 175*n + 441 + 3*(n^2 + 7*n + 29)*(-1)^n + 30*(2*n + 7)*sign(1-n%4+n%2) + 30*sign(2-(n+1)%4-n%2) + 48*((5*n-n^2)%4)*sign(5-n%8))/768 vector(100, n, a(n-1)) \\ Derek Orr, Apr 05 2015 (MAGMA) m:=70; R:=PowerSeriesRing(Integers(), m); Coefficients(R!((1+x^4+x^8-x^2-x^6)/((1+x^4)*(1+x^2)^2*(1+x)^3*(1-x)^4))); // Bruno Berselli, Apr 07 2015 CROSSREFS Sequence in context: A079084 A092323 A244584 * A125002 A285245 A098528 Adjacent sequences:  A092528 A092529 A092530 * A092532 A092533 A092534 KEYWORD nonn,easy AUTHOR N. J. A. Sloane, Apr 08 2004 STATUS approved

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Last modified July 21 04:40 EDT 2019. Contains 325189 sequences. (Running on oeis4.)