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Search: id:A120470
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| A120470 |
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6 X 6 Matrix Markov of the octahedral bonding graph. |
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+0
1
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| 0, 7, 34, 124, 520, 2032, 8224, 32704, 131200, 524032, 2097664, 8387584, 33556480, 134213632, 536879104, 2147467264, 8589967360, 34359672832, 137439084544, 549755551744, 2199023779840, 8796091973632, 35184374185984
(list; graph; listen)
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OFFSET
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0,2
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COMMENT
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Characteristic Polynomial is: x^3*((x-4)*x+2)^2 This result puts the energy levels in reserve order to that found in standard texts in Inorganic Chemistry for d orbitals in octahedral coordination complexex.
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REFERENCES
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Cotton and Wilkinson, Advanced Inorganic Chemistry, Interscience publishers, New York, 1966, page 664, figure 26-4
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FORMULA
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M = {{0, 1, 1, 1, 1, 0}, {1, 0, 1, 0, 1, 1}, {1, 1, 0, 1, 0, 1}, {1, 0, 1, 0, 1, 1}, {1, 1, 0, 1, 0, 1}, {0, 1, 1, 1, 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, 1, 1, 1, 0}, {1, 0, 1, 0, 1, 1}, {1, 1, 0, 1, 0, 1}, {1, 0, 1, 0, 1, 1}, {1, 1, 0, 1, 0, 1}, {0, 1, 1, 1, 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}] Det[M - x*IdentityMatrix[6]] Factor[%] aaa = Table[x /. NSolve[Det[M - x*IdentityMatrix[6]] == 0, x][[n]], {n, 1, 6}] Abs[aaa] a1 = Table[N[a[[n]]/a[[n - 1]]], {n, 7, 50}]
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CROSSREFS
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Sequence in context: A063166 A024817 A071598 this_sequence A036423 A036632 A036639
Adjacent sequences: A120467 A120468 A120469 this_sequence A120471 A120472 A120473
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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), Jul 04 2006
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