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Search: id:A106569
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| A106569 |
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First entry of the vector (M^n)v, where M is the 2 X 2 matrix [[0,4],[1,4]] and v is the column vector [0,1]. |
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+0
1
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| 0, 3, 15, 84, 465, 2577, 14280, 79131, 438495, 2429868, 13464825, 74613729, 413463120, 2291156787, 12696173295, 70354336836, 389860204065, 2160364030833, 11971400766360, 66338095924299, 367604681920575
(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): -0.541381, 5.54138. a(n)=3*A015536(n).
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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, 4], [1, 4]] and v[0] is the column vector [0,1]. a(n)=5a(n-1)+3a(n-2); a(0)=0, a(1)=3.
a(n)=(3/37)*[5/2+(1/2)*sqrt(37)]^n*sqrt(37)-(3/37)*[5/2-(1/2)*sqrt(37)]^n*sqrt(37), with n>=0 [From Paolo P. Lava (ppl(AT)spl.at), Oct 07 2008]
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MAPLE
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a[0]:=0: a[1]:=3: for n from 2 to 23 do a[n]:=5*a[n-1]+3*a[n-2] od: seq(a[n], n=0..23);
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MATHEMATICA
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M = {{0, 3}, {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
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Equals 3*A015536.
Sequence in context: A118356 A074552 A115910 this_sequence A026032 A005809 A067122
Adjacent sequences: A106566 A106567 A106568 this_sequence A106570 A106571 A106572
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KEYWORD
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nonn
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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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