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A109532
a(n)= +a(n-3) +2*a(n-6) +a(n-9).
1
1, 1, 1, 1, 3, 1, 3, 6, 3, 6, 13, 6, 13, 28, 13, 28, 60, 28, 60, 129, 60, 129, 277, 129, 277, 595, 277, 595, 1278, 595, 1278, 2745, 1278, 2745, 5896, 2745, 5896, 12664, 5896, 12664, 27201, 12664, 27201, 58425, 27201, 58425, 125491, 58425, 125491, 269542
OFFSET
0,5
COMMENTS
The recurrence shows that these are actually three interleaved sequences with
the same recurrence (and the same characteristic polynomial).
FORMULA
G.f.: (1+x+x^2+2*x^4+x^7)/(1-x^3-2*x^6-x^9).
MATHEMATICA
M1 = {{0, 1, 0}, {0, 0, 1}, {1, 1, 0}}; M2 = {{0, 1, 1}, {1, 0, 0}, {0, 1, 0}}; M3 = {{0, 1, 0}, {1, 0, 1}, {1, 0, 0}}; M[n_] = If[Mod[n, 3] == 1, M3, If[Mod[n, 3] == 2, M2, M1]]; v[0] = {0, 1, 1}; v[n_] := v[n] = M[n].v[n - 1] a = Table[v[n][[2]], {n, 0, 100}]
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Roger L. Bagula, Jun 18 2005
EXTENSIONS
Definition replaced by recurrence by the Associate Editors of the OEIS, Sep 28 2009
STATUS
approved