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Search: id:A122023
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| A122023 |
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Vacuum Virtual Particle 10 vertex graph as Feynman diagram seen as a 10 X 10 bonding graph vector Matrix Markov: characteristic Polynomial: x^4(-3 + x^2)(8 - 7 x^2 + x^4). |
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+0
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| 0, 1, 3, 11, 29, 109, 283, 795, 2061, 5053, 13099, 30091, 78013, 173453, 449723, 983163, 2549229, 5523677, 14322635, 30887915, 80092061, 172288429, 446745691, 959703003, 2488530381, 5341975549, 13851888235, 29723290699, 77073397885
(list; graph; listen)
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OFFSET
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1,3
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COMMENT
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Calculation of relative energy of ten particle states as secular equation: aaa = Table[x /. NSolve[Det[M - x*IdentityMatrix[10]] == 0, x][[n]], {n, 1, 10}] Sum[2*aaa[[n]], {n, 1, 5}]=-10.5794 The excess energy is about 8*alpha if each vertex is taken as one unit.
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FORMULA
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M = {{0, 1, 0, 0, 0, 0, 0, 0, 0, 0}, {1, 0, 1, 1, 0, 0, 0, 0, 0, 0}, {0, 1, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 1, 0, 0, 1, 1, 0, 0, 0, 0}, {0, 0, 0, 1, 0, 0, 1, 0, 0, 0}, {0, 0, 0, 1, 0, 0, 1, 0, 0, 0}, {0, 0, 0, 0, 1, 1, 0, 0, 1, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 1, 0}, {0, 0, 0, 0, 0, 0, 1, 1, 0, 1}, {0, 0, 0, 0, 0, 0, 0, 0, 1, 0}} v[1] = Table[Fibonacci[n], {n, 0, 9}] 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, 0, 0, 0, 0, 0}, {1, 0, 1, 1, 0, 0, 0, 0, 0, 0}, {0, 1, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 1, 0, 0, 1, 1, 0, 0, 0, 0}, {0, 0, 0, 1, 0, 0, 1, 0, 0, 0}, {0, 0, 0, 1, 0, 0, 1, 0, 0, 0}, {0, 0, 0, 0, 1, 1, 0, 0, 1, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 1, 0}, {0, 0, 0, 0, 0, 0, 1, 1, 0, 1}, {0, 0, 0, 0, 0, 0, 0, 0, 1, 0}} v[1] = Table[Fibonacci[n], {n, 0, 9}] 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: A110954 A000251 A159229 this_sequence A009183 A165893 A106397
Adjacent sequences: A122020 A122021 A122022 this_sequence A122024 A122025 A122026
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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 12 2006
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