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Search: id:A120462
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| A120462 |
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6 X 6 Matrix Markov based on hexagon / benzene chemical bonding type Markov with characteristic polynomial : x^6-6*x^4+9*x^2-4. |
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+0
1
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| 0, 6, 4, 22, 20, 86, 84, 342, 340, 1366, 1364, 5462, 5460, 21846, 21844, 87382, 87380, 349526, 349524, 1398102, 1398100, 5592406, 5592404, 22369622, 22369620, 89478486, 89478484, 357913942, 357913940, 1431655766, 1431655764, 5726623062
(list; graph; listen)
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OFFSET
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0,2
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COMMENT
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Using a Fibonacci starting vector produces a sequence starting at zero. Aromatic benzene like bonding graph of C6H6: Ratio: a[n+1]/a[n]=2 ( here it alternates {1,4}) Inspired by the work of Fan Chung Graham on the Buckyball C60H60 using a benzene bonding 6 X 6 matrix to tile the ball
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REFERENCES
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C5H5 also exists: http://www.ilpi.com/organomet/cp.html
Mathematics and the Buckyball, (this is a somewhat different version from the one that appeared in American Scientist 81, No. 1., (1993) 56-71), (with Shlomo Sternberg).
Groups and the Buckyball, in Lie Theory and Geometry: In honor of Bertram Kostant (Eds. J.-L. Brylinski, R. Brylinski, V. Guillemin and V. Kac) PM 123, Birkhaeuser, Boston, 1994, 97-126, (with Bertram Kostant and Shlomo Sternberg).
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FORMULA
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M = {{0, 1, 0, 0, 0, 1}, {1, 0, 1, 0, 0, 0}, {0, 1, 0, 1, 0, 0}, {0, 0, 1, 0, 1, 0}, {0, 0, 0, 1, 0, 1}, {1, 0, 0, 0, 1, 0}} v[1] = {0, 1, 1, 2, 3, 5} v[n_] := v[n] = M.v[n - 1] a(n) = v[n][[1]]
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MATHEMATICA
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M = {{0, 1, 0, 0, 0, 1}, {1, 0, 1, 0, 0, 0}, {0, 1, 0, 1, 0, 0}, {0, 0, 1, 0, 1, 0}, {0, 0, 0, 1, 0, 1}, {1, 0, 0, 0, 1, 0}} v[1] = {0, 1, 1, 2, 3, 5} 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: A083581 A107983 A009278 this_sequence A061592 A081631 A137174
Adjacent sequences: A120459 A120460 A120461 this_sequence A120463 A120464 A120465
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KEYWORD
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nonn,uned
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AUTHOR
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Roger Bagula and Gary Adamson (rlbagulatftn(AT)yahoo.com), Jun 28 2006
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