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Search: id:A122521
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| A122521 |
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Recursion: a(n) = a(n - 6) + a(n - 8) characteristic Polynomial:x^8-x^2-1. |
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+0
1
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| 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 3, 3, 4, 4, 4, 4, 5, 5, 7, 7, 8, 8, 9, 9, 12, 12, 15, 15, 17, 17, 21, 21, 27, 27, 32, 32, 38, 38, 48, 48, 59, 59, 70, 70, 86, 86, 107, 107, 129, 129, 156, 156, 193, 193, 236, 236, 285, 285, 349, 349, 429, 429, 521, 521, 634, 634, 778, 778
(list; graph; listen)
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OFFSET
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1,9
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COMMENT
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Inspired by the recursion: a(n)=a(n-3)+a(n-4) as power doubled: x^4-x-1-->x^8-x^2-1 Root sum is zero and the ratio of the sequence is very low.
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FORMULA
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a(n) = a(n - 6) + a(n - 8)
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MATHEMATICA
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a[0] = 1; a[1] = 1; a[2] = 1; a[3] = 1; a[4] = 1; a[5] = 1; a[6] = 1; a[7] = 1; a[n_] := a[n] = a[n - 6] + a[n - 8] Table[a[n], {n, 0, 100}] (*vector Matrix Markov*) M = {{0, 1, 0, 0, 0, 0, 0, 0}, {0, 0, 1, 0, 0, 0, 0, 0}, {0, 0, 0, 1, 0, 0, 0, 0}, {0, 0, 0, 0, 1, 0, 0, 0}, {0, 0, 0, 0, 0, 1, 0, 0}, {0, 0, 0, 0, 0, 0, 1, 0}, {0, 0, 0, 0, 0, 0, 0, 1}, {1, 0, 1, 0, 0, 0, 0, 0}}; v[1] = Table[1, {n, 1, 8}] v[n_] := v[n] = M.v[n - 1] a = Table[v[n][[1]], {n, 1, 100}]
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CROSSREFS
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Sequence in context: A029378 A053278 A035466 this_sequence A086394 A029226 A093354
Adjacent sequences: A122518 A122519 A122520 this_sequence A122522 A122523 A122524
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KEYWORD
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nonn,uned
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AUTHOR
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Roger Bagula (rlbagulatftn(AT)yahoo.com), Sep 16 2006
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