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A122058
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Affine vector matrix Markov based on Faddeev's three body T matrix: characteristic polynomial of the matrix is (12 + 11 x - x^3).
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0
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1, 5, 22, 84, 319, 1205, 4534, 17100, 64351, 242525, 913078, 3440004, 12954175, 48796997, 183775990, 692217084, 2607099871, 9819699821, 36984703606, 139301896500, 524668137535, 1976137304789, 7442972270902, 28033528003116
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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COMMENTS
| This affive vector matrix Markov actually produces three distinct sequences, but the "1" sequence in the input particle sequence. The characteristic polynomial has the unique secular characteristic that the sum of the roots is zero and all the roots are real: aaa = Table[x /. NSolve[Det[M - x*IdentityMatrix[3]] == 0, x][[n]], {n, 1, 3}] {-2.48361, -1.28282, 3.76644} Apply[Plus, aaa]=>0
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REFERENCES
| R.G. Newton, Scattering Theory of Waves and Particles,McGraw Hill, New York,1966, Page 557 ff
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FORMULA
| M = {{0, 1, 1}, {2, 0, 2}, {3, 3, 0}}; v[1] = {1, 2, 3}; v[n_] := v[n] = M.v[n - 1] + {0, 2, 3} a(n) = v[n][[1]]
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MATHEMATICA
| M = {{0, 1, 1}, {2, 0, 2}, {3, 3, 0}}; v[1] = {1, 2, 3}; v[n_] := v[n] = M.v[n - 1] + {0, 2, 3} a1 = Table[v[n][[1]], {n, 1, 50}]
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CROSSREFS
| Sequence in context: A058750 A058752 A183925 * A191008 A006148 A086090
Adjacent sequences: A122055 A122056 A122057 * A122059 A122060 A122061
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KEYWORD
| nonn,uned
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AUTHOR
| Roger Bagula (rlbagulatftn(AT)yahoo.com), Sep 14 2006
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