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Search: id:A120723
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| A120723 |
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Let M be the 8 X 8 matrix M = {{0, 1, 1, 0, 0, 1, 0, 0}, {1, 0, 0, 1, 1, 0, 0, 0}, {1, 0, 0, 1, 0, 1, 1, 0}, {0, 1, 1, 0, 1, 0, 1, 0}, {0, 1, 0, 1, 0, 1, 0, 1}, {1, 0, 1, 0, 1, 0, 0, 1}, {0, 0, 1, 1, 0, 0, 0, 1}, {0, 0, 0, 0, 1, 1, 1, 0}}; let v[1] = [Fibonacci[1], ..., Fibonacci[8]]; let v[n] = M.v[n - 1]; then a(n) = v[n][[1]]. |
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+0
1
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| 1, 11, 63, 247, 887, 3207, 11383, 40679, 144663, 515719, 1835831, 6540327, 23289943, 82955975, 295436919, 1052244583, 3747563927, 13347268359, 47536758199, 169305160871, 602988299991, 2147576619847, 7648703663351
(list; graph; listen)
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OFFSET
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1,2
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COMMENT
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8 X 8 Markov chain for N4S4 and As4S4 which has D2d symmetry; characteristic polynomial = 16 - 56 x^2 + 16 x^3 + 45 x^4 - 8 x^5 - 14 x^6 + x^8.
One view of this structure is as a tetrahedron with a square plane in the middle of it.
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REFERENCES
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Cotton and Wilkinson, Advanced Inoraganic Chemistry, Interscience Publishers, New York, 1966, page 533
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MATHEMATICA
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M = {{0, 1, 1, 0, 0, 1, 0, 0}, {1, 0, 0, 1, 1, 0, 0, 0}, {1, 0, 0, 1, 0, 1, 1, 0}, {0, 1, 1, 0, 1, 0, 1, 0}, {0, 1, 0, 1, 0, 1, 0, 1}, {1, 0, 1, 0, 1, 0, 0, 1}, {0, 0, 1, 1, 0, 0, 0, 1}, {0, 0, 0, 0, 1, 1, 1, 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
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Sequence in context: A009016 A052051 A162946 this_sequence A053367 A163706 A054333
Adjacent sequences: A120720 A120721 A120722 this_sequence A120724 A120725 A120726
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KEYWORD
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nonn
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AUTHOR
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Roger Bagula (rlbagulatftn(AT)yahoo.com), Aug 17 2006
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EXTENSIONS
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Edited by N. J. A. Sloane (njas(AT)research.att.com), Jun 15 2007
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