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A123589
Expansion of x*(3*x+1)*(1 - x^2 - x^3)/(1 - x - 15*x^2 - 19*x^3 + 20*x^4).
2
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.
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
KEYWORD
nonn,easy
AUTHOR
STATUS
approved

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Last modified September 20 20:48 EDT 2024. Contains 376078 sequences. (Running on oeis4.)