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Search: id:A052282
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| A052282 |
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Number of 3 X 3 stochastic matrices under row and column permutations. |
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+0
4
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| 1, 1, 3, 5, 9, 13, 22, 30, 45, 61, 85, 111, 149, 189, 244, 304, 381, 465, 571, 685, 825, 977, 1158, 1354, 1585, 1833
(list; graph; listen)
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OFFSET
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0,3
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COMMENT
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Unreduced numerators in convergent to log(2) = lim[n->inf, a(n)/A000670(n+1)].
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FORMULA
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G.f.: (x^6-x^5+x^3-x+1)/[(1-x)^5(1+x)^2(1+x+x^2)]. - Ralf Stephan and Vladeta Jovovic, May 07 2004
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EXAMPLE
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There are 5 nonisomorphic 3 X 3 matrices with row and column sums 3:
[0 0 3] [0 0 3] [0 1 2] [0 1 2] [1 1 1]
[0 3 0] [1 2 0] [1 1 1] [1 2 0] [1 1 1]
[3 0 0] [2 1 0] [2 1 0] [2 0 1] [1 1 1]
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MAPLE
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(Maple) a := n -> (Matrix([[1, 0, 0, 1, 1, 3, 5, 9, 13]]).Matrix(9, (i, j)-> if (i=j-1) then 1 elif j=1 then [2, 1, -3, -1, 1, 3, -1, -2, 1][i] else 0 fi)^n)[1, 1]; seq (a(n), n=0..25); [From Alois P. Heinz (heinz(AT)hs-heilbronn.de), Jul 31 2008]
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CROSSREFS
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Cf. A002817, A052280, A052281. Different from A001993.
Sequence in context: A136252 A141325 A146905 this_sequence A001993 A153263 A133033
Adjacent sequences: A052279 A052280 A052281 this_sequence A052283 A052284 A052285
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KEYWORD
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more,nonn
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AUTHOR
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Vladeta Jovovic (vladeta(AT)eunet.rs), Feb 06 2000
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