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Search: id:A123954
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| A123954 |
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A tridiagonal 5 X 5 vector matrix Markov with 4's on the main diagonal with characteristic polynomial: 780 - 1091 x + 592 x^2 - 156 x^3 + 20 x^4 - x^5. |
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+0
1
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| 0, 0, 0, 0, 1, 20, 244, 2352, 19725, 150996, 1084600, 7438112, 49268857, 317763732, 2007173532, 12470499600, 76456454725, 463727364692, 2787905507488, 16639142746368, 98709193239921, 582627136604436, 3424383528301252
(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 3,4,5 count up in the middle: aaa = Table[x /. NSolve[Det[M - x*IdentityMatrix[5]] == 0, x][[n]], {n, 1, 5}] {2.26795, 3., 4., 5., 5.73205}
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FORMULA
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M = {{4, -1, 0, 0, 0}, {-1, 4, -1, 0, 0}, {0, -1, 4, -1, 0}, {0, 0, -1, 4, -1}, {0, 0, 0, -1, 4}}; v[1] = {0, 0, 0, 0, 1}; v[n_] := v[n] = M.v[n - 1]; a(n) = v[n][[1]]
G.f.: -x^5/((4*x-1)*(3*x-1)*(5*x-1)*(13*x^2-8*x+1)) [From Maksym Voznyy (voznyy(AT)mail.ru), Jul 28 2009]
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MATHEMATICA
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M = {{4, -1, 0, 0, 0}, {-1, 4, -1, 0, 0}, {0, -1, 4, -1, 0}, {0, 0, -1, 4, -1}, {0, 0, 0, -1, 4}}; 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: A040075 A138442 A140124 this_sequence A125432 A055757 A022744
Adjacent sequences: A123951 A123952 A123953 this_sequence A123955 A123956 A123957
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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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