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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
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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COMMENTS
| d=2: Z/2Z by this methods is:A000129 Pell numbers
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FORMULA
| 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].
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MATHEMATICA
| 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
| Cf. A095897, A000129.
Sequence in context: A145054 A166839 A166827 * A183320 A180326 A119085
Adjacent sequences: A138050 A138051 A138052 * A138054 A138055 A138056
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KEYWORD
| nonn
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AUTHOR
| Roger L. Bagula and Gary Adamson (rlbagulatftn(AT)yahoo.com), May 02 2008
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