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Search: id:A122994
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| A122994 |
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A rational vector matrix Markov with 1/3 coefficient: characteristic Polynomial: -1 - x/3 + x^2. |
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+0
4
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| 1, 3, 12, 39, 147, 498, 1821, 6303, 22692, 79419, 283647, 998418, 3551241, 12537003, 44498172, 157331199, 557814747, 1973795538, 6994128261, 24758288103, 87705442452, 310530035379, 1099879017447, 3894649335858, 13793560492881
(list; graph; listen)
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OFFSET
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1,2
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COMMENT
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Two real roots: NSolve[Det[M - x*IdentityMatrix[2]] == 0, x] {{x -> -0.847127}, {x -> 1.18046}}
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FORMULA
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M := {{0, 1}, {1, 1/3}}; v[1] = {1, 1}; v[n_] := v[n] = M.v[n - 1]; a(n) =v[n][[1]]*3^(n - 1)
a(n)=a(n-1)+9*a(n-2). [From Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Mar 26 2009]
G.f.: -x*(1+2*x)/(-1+x+9*x^2). a(n)= A015445(n-1)+2*A015445(n-2). [From R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Aug 12 2009]
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MATHEMATICA
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M := {{0, 1}, {1, 1/3}}; v[1] = {1, 1}; v[n_] := v[n] = M.v[n - 1]; a = Table[v[n][[1]]*3^(n - 1), {n, 1, 30}]
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CROSSREFS
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Cf. A026597.
Sequence in context: A029858 A123109 A110153 this_sequence A062311 A034956 A032093
Adjacent sequences: A122991 A122992 A122993 this_sequence A122995 A122996 A122997
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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), Sep 22 2006
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