A157876 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)).

1, -1, 1, -1, 1, -2, 2, -3, 4, -6, 9, -12, 17, -22, 30, -40, 54, -74, 100, -138, 188, -258, 352, -479, 653, -887, 1209, -1645, 2242, -3056, 4165, -5680, 7740, -10551, 14376, -19589, 26692, -36368, 49560, -67532, 92032, -125416, 170912, -232912, 317392

Offset

0,6

Comments

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

References

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

Links

Table of n, a(n) for n=0..44.

Index entries for linear recurrences with constant coefficients, signature (-1,0,0,0,-1,-1,-1,0,-1,0,-1).

Formula

O.g.f.: 1/(x^11+x^9+x^7+x^6+x^5+x+1). - Georg Fischer, Apr 18 2022

Mathematica

f[x_] = 1 + x^2 + x^4 + x^5 + x^6 + x^10 + x^11;
g[x] = ExpandAll[x^11*f[1/x]];
a = Table[SeriesCoefficient[ Series[1/g[x], {x, 0, 50}], n], {n, 0, 50}]

Crossrefs

Sequence in context: A068106 A186964 A005856 * A289433 A351973 A212264

Adjacent sequences: A157873 A157874 A157875 * A157877 A157878 A157879

Keyword

sign,easy

Author

Roger L. Bagula, Mar 08 2009

Extensions

Edited by N. J. A. Sloane, Sep 04 2010

Status

approved