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Search: id:A109528
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| A109528 |
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a(n)= 3*a(n-3) +3*a(n-6) +a(n-9). |
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3
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| 0, 1, 3, 1, 2, 12, 2, 9, 45, 9, 34, 174, 34, 131, 669, 131, 504, 2574, 504, 1939, 9903, 1939, 7460, 38100, 7460, 28701, 146583, 28701, 110422, 563952, 110422, 424829, 2169705, 424829, 1634454, 8347554, 1634454, 6288271, 32115729, 6288271
(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 this consists of three interleaved sequences (actually two, one doubled) with the same recurrence (and the same characteristic polynomial).
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FORMULA
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G.f.: x*(-1-3*x-x^2+x^3-3*x^4+x^5)/(-1+3*x^3+3*x^6+x^9). [From R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Sep 27 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][[1]], {n, 0, 100}]
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CROSSREFS
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Cf. A000931.
Sequence in context: A144156 A116854 A016567 this_sequence A136125 A092580 A004468
Adjacent sequences: A109525 A109526 A109527 this_sequence A109529 A109530 A109531
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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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Defintion replaced by recurrence. - The Assoc. Editors of the OEIS, Oct 22 2009
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