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A106567
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First entry of the vector (M^n)v, where M is the 2 X 2 matrix [[0,4],[1,5]] and v is the column vector [0,1].
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0
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0, 4, 20, 116, 660, 3764, 21460, 122356, 697620, 3977524, 22678100, 129300596, 737215380, 4203279284, 23965257940, 136639406836, 779058065940, 4441847957044, 25325472048980, 144394752073076, 823275648561300
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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COMMENTS
| Real Pisot roots (the eigenvalues of M): -0.701562, 5.70156.
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FORMULA
| a(n)=first entry of v[n], where v[n]=Mv[n-1], M is the 2 X 2 matrix [[0, 4], [1, 5]] and v[0] is the column vector [0,1].
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MAPLE
| with(linalg): M:=matrix(2, 2, [0, 4, 1, 5]): v[0]:=matrix(2, 1, [0, 1]): for n from 1 to 20 do v[n]:=multiply(M, v[n-1]) od: seq(v[n][1, 1], n=0..20);
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MATHEMATICA
| M = {{0, 4}, {1, 5}} v[1] = {0, 1} v[n_] := v[n] = M.v[n - 1] a = Table[v[n][[1]], {n, 1, 50}]
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CROSSREFS
| Equals 4*A015537.
Sequence in context: A171802 A100034 A192924 * A077445 A085458 A085456
Adjacent sequences: A106564 A106565 A106566 * A106568 A106569 A106570
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KEYWORD
| nonn
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AUTHOR
| Roger L. Bagula (rlbagulatftn(AT)yahoo.com), May 30 2005
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EXTENSIONS
| Edited by N. J. A. Sloane (njas(AT)research.att.com), Apr 30 2006
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