A123589 Expansion of x*(3*x+1)*(1 - x^2 - x^3)/(1 - x - 15*x^2 - 19*x^3 + 20*x^4).

1, 4, 18, 93, 416, 2073, 9720, 46859, 223726, 1069831, 5121642, 24482721, 117159620, 560315013, 2680448172, 12821551727, 61331067154, 293376558067, 1403343084750, 6712850697141, 32110530228584, 153599278134609

Offset

1,2

Comments

Sum of the top row elements of the n-th matrix power of the 9 X 9 matrix shown in the Mathematica program.

Links

G. C. Greubel, Table of n, a(n) for n = 1..1000

Index entries for linear recurrences with constant coefficients, signature (1, 15, 19, -20).

Mathematica

M = {{0, 1, 1, 0, 1, 0, 0, 1, 0}, {1, 0, 1, 0, 0, 1, 0, 0, 1}, {1, 1, 0, 1, 1, 0, 1, 1, 0}, {0, 1, 0, 0, 1, 1, 0, 1, 0}, {0, 0, 1, 1, 0, 1, 0, 0, 1}, {1, 1, 0, 1, 1, 1, 1, 1, 0}, {0, 1, 0, 0, 1, 0, 0, 1, 1}, {0, 0, 1, 0, 0, 1, 1, 0, 1}, {1, 1, 0, 1, 1, 0, 1, 1, 0}}; v[1] = {1, 1, 1, 1, 1, 1, 1, 1, 1}; v[n_] := v[n] = M.v[n - 1]; a = Table[Floor[v[n][[1]]], {n, 1, 50}]
Rest[CoefficientList[Series[x*(3*x + 1)*(1 - x^2 - x^3)/(1 - x - 15*x^2 - 19*x^3 + 20*x^4), {x, 0, 50}], x]] (* G. C. Greubel, Oct 16 2017 *)

Prog

(PARI) Vec(x*(3*x+1)*(1-x^2-x^3)/(1-x-15*x^2-19*x^3+20*x^4)+O(x^99)) \\ Charles R Greathouse IV, Sep 27 2012

Crossrefs

Cf. A120658.

Sequence in context: A081923 A020064 A306153 * A245103 A200717 A346763

Adjacent sequences: A123586 A123587 A123588 * A123590 A123591 A123592

Keyword

nonn,easy

Author

Roger L. Bagula and Gary W. Adamson, Nov 12 2006

Status

approved