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Search: id:A123184
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| A123184 |
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A linear sum zero 9 X 9 matrix Markov: characteristic polynomial: (-3 + x)(-1 + x) x^3 (-1 + 3 x + 27 x^2 - 12 x^3 + x^4). |
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+0
1
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| 1, 1, 3, 15, 103, 829, 7131, 62901, 559897, 4999879, 44699763, 399783639, 3576070333, 31989586339, 286166485929, 2559950572641, 22900519062931, 204861053422423, 1832624941137951, 16394109244633845, 146656754883677131
(list; graph; listen)
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OFFSET
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1,3
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COMMENT
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A Hadamard self-similar matrix of m: m={{1, -1, 0}, {-1, 2, -1}, {0, -1, 1}}.{1,1,1}={0,0,0} 9 X 9 is: {{m,-m,0}, {-m,2*m-m}, {0,-m,m}} A signed version of A011782 is an 6 X 6: {{-m,m}, {m,-m}}
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FORMULA
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M = {{-1, 1, 0, 1, -1, 0}, {1, -2, 1, -1, 2, -1}, {0, 1, -1, 0, -1, 1}, {1, -1, 0, -1, 1, 0}, {-1, 2, -1, 1, -2, 1}, {0, -1, 1, 0, 1, -1}} v[1] = {1, 0, 0, 0, 0, 1} v[n_] := v[n] = M.v[n - 1] a(n) = v[n][[1]]
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MATHEMATICA
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M = {{-1, 1, 0, 1, -1, 0}, {1, -2, 1, -1, 2, -1}, {0, 1, -1, 0, -1, 1}, {1, -1, 0, -1, 1, 0}, {-1, 2, -1, 1, -2, 1}, {0, -1, 1, 0, 1, -1}} v[1] = {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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Cf. A011782.
Sequence in context: A152093 A109777 A135903 this_sequence A079486 A001274 A139766
Adjacent sequences: A123181 A123182 A123183 this_sequence A123185 A123186 A123187
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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), Oct 02 2006
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