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Search: id:A106709
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| A106709 |
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First entry of the vector (M^n)v, where M is the 2 X 2 matrix [[0,-2],[1,5]] and v is the column vector [0,1]. |
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| 0, -2, -10, -46, -210, -958, -4370, -19934, -90930, -414782, -1892050, -8630686, -39369330, -179585278, -819187730, -3736768094, -17045465010, -77753788862, -354678014290, -1617882493726, -7380056440050, -33664517212798, -153562473183890
(list; graph; listen)
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OFFSET
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0,2
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COMMENT
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Real Pisot roots (the eigenvalues of M): 0.438447, 4.56155.
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FORMULA
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a(n)=first entry of v[n], where v[n]=Mv[n-1], M is the 2 X 2 matrix [[0, -2], [1, 5]] and v[0] is the column vector [0,1].
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MAPLE
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with(linalg): M:=matrix(2, 2, [0, -2, 1, 5]): v[0]:=matrix(2, 1, [0, 1]): for n from 1 to 22 do v[n]:=multiply(M, v[n-1]) od: seq(v[n][1, 1], n=0..22);
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MATHEMATICA
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M = {{0, -2}, {1, 5}} v[1] = {0, 1} v[n_] := v[n] = M.v[n - 1] a = Table[Abs[v[n][[1]]], {n, 1, 50}]
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CROSSREFS
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Adjacent sequences: A106706 A106707 A106708 this_sequence A106710 A106711 A106712
Sequence in context: A137334 A080643 A032389 this_sequence A137193 A006213 A137635
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KEYWORD
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sign
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AUTHOR
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Roger L. Bagula (rlbagulatftn(AT)yahoo.com), May 30 2005
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EXTENSIONS
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Edited by N. J. A. Sloane (njas(AT)research.att.com), Apr 30 2006
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