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 A109531 a(n)= +a(n-3) +2*a(n-6) +a(n-9). 2
 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; text; internal format)
 OFFSET 0,6 COMMENTS The recurrence shows that these are actually three interleaved sequences with the same recurrence (and the same characteristic polynomial). LINKS Table of n, a(n) for n=0..50. Index entries for linear recurrences with constant coefficients, signature (0,0,1,0,0,2,0,0,1). 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] 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}] LinearRecurrence[{0, 0, 1, 0, 0, 2, 0, 0, 1}, {0, 1, 1, 1, 1, 4, 1, 3, 7}, 70] (* Harvey P. Dale, Apr 10 2022 *) CROSSREFS Cf. A000931, A109532, A109533. Sequence in context: A151861 A210583 A200171 * A200132 A073817 A074081 Adjacent sequences: A109528 A109529 A109530 * A109532 A109533 A109534 KEYWORD nonn,easy AUTHOR Roger L. Bagula, Jun 18 2005 EXTENSIONS Definition replaced by recurrence by the Associate Editors of the OEIS, Sep 28 2009 STATUS approved

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Last modified April 23 09:45 EDT 2024. Contains 371905 sequences. (Running on oeis4.)