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Let f(x) = 1 + x^2 + x^4 + x^5 + x^6 + x^10 + x^11; sequence has g.f. g(x) = 1/(x^11*f(1/x)).
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%I #10 Apr 19 2023 02:26:37

%S 1,-1,1,-1,1,-2,2,-3,4,-6,9,-12,17,-22,30,-40,54,-74,100,-138,188,

%T -258,352,-479,653,-887,1209,-1645,2242,-3056,4165,-5680,7740,-10551,

%U 14376,-19589,26692,-36368,49560,-67532,92032,-125416,170912,-232912,317392

%N Let f(x) = 1 + x^2 + x^4 + x^5 + x^6 + x^10 + x^11; sequence has g.f. g(x) = 1/(x^11*f(1/x)).

%C x^23+1 factors mod 2 into (x+1)*f(x)*g(x).

%D J. H. Conway and N. J. A. Sloane, "Sphere Packings, Lattices and Groups", Springer-Verlag, pp. 231.

%H <a href="/index/Rec#order_11">Index entries for linear recurrences with constant coefficients</a>, signature (-1,0,0,0,-1,-1,-1,0,-1,0,-1).

%F O.g.f.: 1/(x^11+x^9+x^7+x^6+x^5+x+1). - _Georg Fischer_, Apr 18 2022

%t f[x_] = 1 + x^2 + x^4 + x^5 + x^6 + x^10 + x^11;

%t g[x] = ExpandAll[x^11*f[1/x]];

%t a = Table[SeriesCoefficient[ Series[1/g[x], {x, 0, 50}], n], {n, 0, 50}]

%K sign,easy

%O 0,6

%A _Roger L. Bagula_, Mar 08 2009

%E Edited by _N. J. A. Sloane_, Sep 04 2010