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Search: id:A109533
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| A109533 |
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a(n)= +a(n-3) +2*a(n-6) +a(n-9). |
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+0
3
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| 1, 0, 1, 2, 1, 3, 5, 1, 6, 10, 3, 13, 22, 6, 28, 47, 13, 60, 101, 28, 129, 217, 60, 277, 466, 129, 595, 1001, 277, 1278, 2150, 595, 2745, 4618, 1278, 5896, 9919, 2745, 12664, 21305, 5896, 27201, 45761, 12664, 58425, 98290, 27201, 125491, 211117, 58425
(list; graph; listen)
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OFFSET
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0,4
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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+x^2+x^3+x^4+2*x^5+x^6+x^8)/(1-x^3-2*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, 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][[3]], {n, 0, 100}]
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CROSSREFS
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Cf. A000931, A109531, A109523.
Sequence in context: A124819 A124019 A125076 this_sequence A062705 A059234 A120852
Adjacent sequences: A109530 A109531 A109532 this_sequence A109534 A109535 A109536
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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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