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Search: id:A109529
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| A109529 |
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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, 2, 1, 2, 9, 2, 9, 34, 9, 34, 131, 34, 131, 504, 131, 504, 1939, 504, 1939, 7460, 1939, 7460, 28701, 7460, 28701, 110422, 28701, 110422, 424829, 110422, 424829, 1634454, 424829, 1634454, 6288271, 1634454, 6288271, 24193004, 6288271, 24193004
(list; graph; listen)
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OFFSET
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0,2
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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+x^2-x^3+3*x^4-x^5+x^7)/(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][[2]], {n, 0, 100}]
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CROSSREFS
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Cf. A000213, A109528, A109530.
Sequence in context: A137305 A143208 A119419 this_sequence A022694 A002079 A078357
Adjacent sequences: A109526 A109527 A109528 this_sequence A109530 A109531 A109532
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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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