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Search: id:A123955
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| A123955 |
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A tridiagonal 5 X 5 vector matrix Markov with 3's on the main diagonal with characteristic polynomial: 144 - 300 x + 234 x^2 - 86 x^3 + 15 x^4 - x^5). |
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+0
1
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| 0, 0, 0, 0, 1, 15, 139, 1029, 6691, 40041, 226435, 1230009, 6487195, 33464145, 169720915, 849504825, 4208146411, 20674387905, 100901918659, 489826044489, 2367517203931, 11402423910801, 54755709794995, 262308279256089
(list; graph; listen)
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OFFSET
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1,6
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COMMENT
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All the roots are large positive with a 2,3,4 count up in the middle: aaa = Table[x /. NSolve[Det[M - x*IdentityMatrix[5]] == 0, x][[n]], {n, 1, 5}] {1.26795, 2., 3., 4., 4.73205}
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FORMULA
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M = {{3, -1, 0, 0, 0}, {-1, 3, -1, 0, 0}, {0, -1, 3, -1, 0}, {0, 0, -1, 3, -1}, {0, 0, 0, -1, 3}}; v[1] = {0, 0, 0, 0, 1}; v[n_] := v[n] = M.v[n - 1]; a(n) = v[n][[1]]
G.f.: -x^5/((3*x-1)*(2*x-1)*(4*x-1)*(6*x^2-6*x+1)) [From Maksym Voznyy (voznyy(AT)mail.ru), Jul 28 2009]
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MATHEMATICA
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M = {{3, -1, 0, 0, 0}, {-1, 3, -1, 0, 0}, {0, -1, 3, -1, 0}, {0, 0, -1, 3, -1}, {0, 0, 0, -1, 3}}; v[1] = {0, 0, 0, 0, 1}; v[n_] := v[n] = M.v[n - 1]; a1 = Table[v[n][[1]], {n, 1, 50}]
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CROSSREFS
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Sequence in context: A155648 A126536 A030056 this_sequence A027802 A133716 A035330
Adjacent sequences: A123952 A123953 A123954 this_sequence A123956 A123957 A123958
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KEYWORD
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nonn,uned,probation
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AUTHOR
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Gary Adamson and Roger Bagula (rlbagulatftn(AT)yahoo.com), Oct 27 2006
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EXTENSIONS
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G.f. proposed by Maksym Voznyy checked and corrected by R. J. Mathar, Sep 16 2009.
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