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A109531
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a(n)= +a(n-3) +2*a(n-6) +a(n-9).
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2
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0, 1, 1, 1, 1, 4, 1, 3, 7, 3, 6, 16, 6, 13, 34, 13, 28, 73, 28, 60, 157, 60, 129, 337, 129, 277, 724, 277, 595, 1555, 595, 1278, 3340, 1278, 2745, 7174, 2745, 5896, 15409, 5896, 12664, 33097, 12664, 27201, 71089, 27201, 58425, 152692, 58425, 125491, 327967
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,6
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COMMENTS
| The recurrence shows that these are actually three interleaved sequences with
the same recurrence (and the same characteristic polynomial).
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FORMULA
| G.f.: -x*(x^2-x+1)*(x^5+x^4+2*x^2+2*x+1)/(-1+x^3+2*x^6+x^9). [Sep 28 2009]
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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][[1]], {n, 0, 100}]
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CROSSREFS
| Cf. A000931, A109532, A109533.
Sequence in context: A074813 A151861 A200171 * A200132 A073817 A074081
Adjacent sequences: A109528 A109529 A109530 * A109532 A109533 A109534
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KEYWORD
| nonn,easy
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AUTHOR
| Roger L. Bagula (rlbagulatftn(AT)yahoo.com), Jun 18 2005
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EXTENSIONS
| Definition replaced by recurrence by the Associate Editors of the OEIS, Sep 28 2009
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