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Search: id:A122006
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| A122006 |
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3 X 3 addition table taken as vector matrix Markov to give three parallel sequences: second sequence characteristic polynomial: -(-3+x)*(-3+x^2). |
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+0
3
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| 0, 1, 2, 9, 24, 81, 234, 729, 2160, 6561, 19602, 59049, 176904, 531441, 1593594, 4782969, 14346720, 43046721, 129133602, 387420489, 1162241784, 3486784401, 10460294154, 31381059609, 94143001680, 282429536481, 847288078002
(list; graph; listen)
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OFFSET
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1,3
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COMMENT
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Limit[a[n+1]/a[n],n->Infinity]=3
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REFERENCES
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"Linear Algebra, Examples and Applications" by Alain M. Robert, World Scientific, 2005, p. 58.
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FORMULA
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M = {{0, 1, 2}, {1, 2, 0}, {2, 0, 1}} v[1] = {1, 0, 0} v[n_] := v[n] = M.v[n - 1] a(n) = v[n][[2]]
G.f.: x^2*(1-x)/((1-3x)(1-3x^2)). a(n)=3a(n-1)+3a(n-2)-9a(n-3) . [From Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Mar 09 2009]
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MATHEMATICA
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M = {{0, 1, 2}, {1, 2, 0}, {2, 0, 1}} v[1] = {1, 0, 0} v[n_] := v[n] = M.v[n - 1] a1 = Table[v[n][[2]], {n, 1, 50}]
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CROSSREFS
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Cf. A007179 [From Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Mar 09 2009]
Sequence in context: A023662 A131357 A079997 this_sequence A143561 A027302 A073981
Adjacent sequences: A122003 A122004 A122005 this_sequence A122007 A122008 A122009
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KEYWORD
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nonn,uned
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AUTHOR
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Roger Bagula and Gary Adamson (rlbagulatftn(AT)yahoo.com), Sep 11 2006
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