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A122006
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Expansion of x^2*(1-x)/((1-3*x)*(1-3*x^2)).
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2
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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; refs; listen; history; internal format)
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OFFSET
| 1,3
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COMMENTS
| Limit(n->infinity) a(n+1)/a(n)=3.
The sequence can be created by multiplying the n-th power of the matrix [[0,1,2],[1,2,0],[2,0,1]], multiplying from the right with the vector [1,0,0] and taking the middle element of the resulting vector.
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REFERENCES
| Alain M. Robert, "Linear Algebra, Examples and Applications", World Scientific, 2005, p. 58.
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LINKS
| Index to sequences with linear recurrences with constant coefficients, signature (3,3,-9).
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FORMULA
| 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
| 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
| Cf. A007179 [From Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Mar 09 2009]
Sequence in context: A023662 A131357 A079997 * A200086 A143561 A027302
Adjacent sequences: A122003 A122004 A122005 * A122007 A122008 A122009
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KEYWORD
| nonn,easy
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AUTHOR
| Roger Bagula and Gary Adamson (rlbagulatftn(AT)yahoo.com), Sep 11 2006
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