A167177 Expansion of 1/((1 +x +x^2)^2 *(1 +x^2 +x^3)^3).

1, -2, -2, 5, 5, -7, -13, 2, 29, 19, -47, -68, 43, 151, 31, -246, -237, 267, 611, -34, -1078, -707, 1327, 2149, -701, -4118, -1760, 5611, 6904, -4361, -14463, -3123, 21453, 20320, -20510, -47501, -426, 76389, 54711, -84119, -147200, 30748, 256922, 132152, -315913, -432648, 196632

Offset: 0

Author

Roger L. Bagula, Oct 29 2009

Keywords

• sign

Links

• G. C. Greubel, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (-2, -6, -11, -19, -27, -34, -38, -36, -30, -21, -12, -5, -1).

Crossrefs

Cf. A099254.

Programs

Mathematica

a = {t^2 + t + 1, tau^2 + tau + 1, x^3 + x + 1, y^3 + y + 1, z^3 + z + 1} /. y -> x /. z -> x /. t -> x /. tau -> x
p[x_] = Product[a[[n]], {n, 1, 5}]
q[x_] = Expand[x^13*p[1/x]]
Table[ SeriesCoefficient[ Series[1/q[x], {x, 0, 30}], n], {n, 0, 30}]
CoefficientList[Series[1/((1 + x + x^2)^2*(1 + x^2 + x^3)^3), {x, 0, 100}], x] (* G. C. Greubel, Jun 04 2016 *)

Formula

a(n) = -2*a(n-1) -6*a(n-2) -11*a(n-3) -19*a(n-4) -27*a(n-5) -34*a(n-6) -38*a(n-7) -36*a(n-8) -30*a(n-9) -21*a(n-10) -12*a(n-11) -5*a(n-12) -a(n-13).