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A138053
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Sequence generated from the Z/4Z addition table considered as a matrix.
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0
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0, 55, 510, 8931, 125082, 1914687, 28427814, 427716315, 6405522930, 96128646615, 1441565232030, 21625116326451, 324363664692522, 4865513805027567, 72982236661089174, 1094735666472619275, 16421018067720814050
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OFFSET
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1,2
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COMMENTS
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d=2: Z/2Z by this method is A000129 (the Pell numbers).
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LINKS
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Table of n, a(n) for n=1..17.
Index entries for linear recurrences with constant coefficients, signature (12,93,-576,-2592,5184,19440).
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FORMULA
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Let M = the Z/6Z = {0, 1, 2, 3,4,5} addition table considered as a matrix = {{0, 1, 2, 3, 4, 5}, {1, 2, 3, 4, 5, 0}, {2, 3, 4, 5, 0, 1}, {3, 4, 5, 0, 1, 2}, {4, 5, 0, 1, 2, 3}, {5, 0, 1, 2, 3, 4}}. Then a(n) = 2nd term from left in M^n * [0,1,1,3,4,5].
G.f.: -x^2*(19440*x^4+2160*x^3-2304*x^2-150*x+55) /((3*x+1)*(6*x-1)*(6*x+1)*(15*x-1)*(12*x^2-1)). [Colin Barker, Dec 06 2012]
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MATHEMATICA
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Clear[d, M, v, w, a] (* based on A095897 *) d = 6 (* general matrix*) M = Table[Mod[n + m, 6], {n, 0, d - 1}, {m, 0, d - 1}] (* count up start vector*) v = Table[n, {n, 0, d - 1}] {0, 1, 2, 3, 4, 5} (* vector Markov*) w[n_] := MatrixPower[M, n].v a = Table[w[n][[1]], {n, 0, 20}]
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CROSSREFS
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Cf. A095897, A000129.
Sequence in context: A266035 A241699 A262103 * A183320 A185028 A222797
Adjacent sequences: A138050 A138051 A138052 * A138054 A138055 A138056
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KEYWORD
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nonn,easy
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AUTHOR
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Roger L. Bagula and Gary W. Adamson, May 02 2008
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STATUS
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approved
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