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Search: id:A109530
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| A109530 |
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a(n)= 3*a(n-3) +3*a(n-6) +a(n-9). |
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+0
2
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| 1, 0, 2, 6, 1, 9, 23, 2, 34, 88, 9, 131, 339, 34, 504, 1304, 131, 1939, 5017, 504, 7460, 19302, 1939, 28701, 74261, 7460, 110422, 285706, 28701, 424829, 1099203, 110422, 1634454, 4228988, 424829, 6288271, 16270279, 1634454, 24193004, 62597004
(list; graph; listen)
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OFFSET
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0,3
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COMMENT
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The recurrence shows that these are actually three interleaved sequences with
the same recurrence (and the same characteristic polynomial).
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FORMULA
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G.f.: (1+2*x^2+3*x^3+x^4+3*x^5+2*x^6-x^7+x^8)/(1-3*x^3-3*x^6-x^9). [Sep 28 2009]
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MATHEMATICA
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M1 = {{0, 1, 0}, {0, 0, 1}, {1, 1, 1}}; M2 = {{1, 1, 1}, {1, 0, 0}, {0, 1, 0}}; M3 = {{0, 1, 0}, {1, 1, 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][[3]], {n, 0, 100}]
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CROSSREFS
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Cf. A000213, A109529 A109528.
Sequence in context: A011041 A100831 A136763 this_sequence A111519 A008855 A132181
Adjacent sequences: A109527 A109528 A109529 this_sequence A109531 A109532 A109533
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KEYWORD
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nonn,easy
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AUTHOR
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Roger L. Bagula (rlbagulatftn(AT)yahoo.com), Jun 18 2005
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EXTENSIONS
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Definition replaced by recurrence by the Associate Editors of the OEIS, Sep 28 2009
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