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
KEYWORD
nonn,easy
AUTHOR
Roger L. Bagula and Gary W. Adamson, Nov 12 2006
STATUS
approved