A110686 Expansion of (2*x+1)*(4*x^2+8*x+1) / ((x-1)*(3*x^2+3*x+1)*(2*x^3+2*x^2+4*x+1)).

-1, -4, 14, -49, 158, -538, 1877, -6688, 24026, -86557, 311882, -1123270, 4043813, -14554252, 52377062, -188485501, 678287318, -2440910842, 8784002237, -31610714104, 113756642690, -409373197645, 1473201178034, -5301572184286, 19078633788629

Offset

0,2

Links

G. C. Greubel, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (-6,-10,-3,8,6,6).

Formula

a(n) = -6*a(n-1) - 10*a(n-2) - 3*a(n-3) + 8*a(n-4) + 6*a(n-5) + 6*a(n-6) for n>5. - Colin Barker, May 19 2019

Maple

seriestolist(series((2*x+1)*(4*x^2+8*x+1)/((x-1)*(3*x^2+3*x+1)*(2*x^3+2*x^2+4*x+1)), x=0, 25)); -or- Floretion Algebra Multiplication Program, FAMP Code: tessum(infty)-4basekforsumseq[ + 'i - .25'j + .25'k - .25j' + .25k' - .5'ii' - .25'ij' - .25'ik' - .25'ji' - .25'ki' - .5e], Sumtype is set to: sum[Y[15]] = sum[ * ], Fortype is set to: 1A.

Mathematica

CoefficientList[Series[(2*x + 1)*(4*x^2 + 8*x + 1)/((x - 1)*(3*x^2 + 3*x + 1)*(2*x^3 + 2*x^2 + 4*x + 1)), {x, 0, 50}], x] (* G. C. Greubel, Sep 06 2017 *)

Prog

(PARI) Vec((2*x+1)*(4*x^2+8*x+1)/((x-1)*(3*x^2+3*x+1)*(2*x^3+2*x^2+4*x+1))+O(x^99)) \\ Charles R Greathouse IV, Sep 26 2012

Crossrefs

Cf. A110683, A110684, A110685.

Sequence in context: A356121 A345326 A327610 * A071729 A278692 A071733

Adjacent sequences: A110683 A110684 A110685 * A110687 A110688 A110689

Keyword

sign,easy

Author

Creighton Dement, Aug 02 2005

Status

approved