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A122014
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Semi-Linear ( two branches) twist isomer bonding 8 X 8 matrix Markov : Characteristic polynomial: (1 - 7 x^2 + 13 x^4 - 7 x^6 + x^8)=(1 + x - 3 x^2 - x^3 + x^4)(1 - x - 3 x^2 +x^3 + x^4).
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1
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1, 11, 40, 42, 179, 181, 773, 790, 3363, 3460, 14705, 15175, 64448, 66594, 282739, 292313, 1240921, 1283234, 5447271, 5633552, 23913649, 24732419, 104984728, 108581082, 460905635, 476697757, 2023486253, 2092823614, 8883609963
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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COMMENTS
| Bonding like: C-A-B-D | | | | H F G E It's interesting because the result permutates the second bonding set (EFGH) to (FGHE) as a twist and the result although technically the same in Matrix bonding graph terms gives a different output sequence at the same secular roots. This kind of behavior is characteristic of optical isomers.
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FORMULA
| M = {{0, 1, 1, 0, 0, 1, 0, 0}, {1, 0, 0, 1, 0, 0, 1, 0}, {1, 0, 0, 0, 0, 0, 0, 1}, {0, 1, 0, 0, 1, 0, 0, 0}, {0, 0, 0, 1, 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}} v[1] = Table[Fibonacci[n], {n, 1, 8}] v[n_] := v[n] = M.v[n - 1] a(n) =v[n][[1]]
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MATHEMATICA
| M = {{0, 1, 1, 0, 0, 1, 0, 0}, {1, 0, 0, 1, 0, 0, 1, 0}, {1, 0, 0, 0, 0, 0, 0, 1}, {0, 1, 0, 0, 1, 0, 0, 0}, {0, 0, 0, 1, 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}} v[1] = Table[Fibonacci[n], {n, 1, 8}] v[n_] := v[n] = M.v[n - 1] a = Table[Floor[v[n][[1]]], {n, 1, 50}]
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CROSSREFS
| Sequence in context: A138050 A183940 A077568 * A031427 A147296 A059142
Adjacent sequences: A122011 A122012 A122013 * A122015 A122016 A122017
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KEYWORD
| nonn,uned
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AUTHOR
| Roger Bagula (rlbagulatftn(AT)yahoo.com), Sep 11 2006
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