A157746 - OEIS

%I #11 Dec 29 2023 19:01:05

%S 1,0,-1,0,0,-1,0,2,1,-1,-1,-1,-1,0,2,4,2,-4,-6,-2,0,2,10,11,-4,-17,

%T -14,-4,7,22,30,11,-31,-57,-35,15,56,80,64,-32,-152,-160,-28,136,240,

%U 228,29,-312,-521,-324,208,691,784,358,-523,-1401,-1417,-149,1631,2560,1826,-492,-3366,-4692

%N Expansion of 1/(x^11 + x^10 + x^6 + x^5 + x^4 + x^2 + 1).

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

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

%F G.f.: 1/(x^11 + x^10 + x^6 + x^5 + x^4 + x^2 + 1).

%F a(n) + a(n-2) + a(n-4) + a(n-5) + a(n-6) + a(n-10) + a(n-11) = 0. - _Wesley Ivan Hurt_, Dec 29 2023

%t f[x_] = 1 + x + x^5 + x^6 + x^7 + x^9 + 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 0,8

%A _Roger L. Bagula_, Mar 05 2009

%E New name, _Joerg Arndt_, Mar 20 2013