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Search: id:A106435
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| A106435 |
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a(n) = 3*a(n-1)+3*a(n-2), a(0)=0, a(1)=3. |
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+0
1
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| 0, 3, 9, 36, 135, 513, 1944, 7371, 27945, 105948, 401679, 1522881, 5773680, 21889683, 82990089, 314639316, 1192888215, 4522582593, 17146412424, 65006985051, 246460192425, 934401532428, 3542585174559, 13430960120961
(list; graph; listen)
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OFFSET
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1,2
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COMMENT
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The first entry of the vector v[n]=Mv[n-1], where M is the 2 x 2 matrix [[0,3],[1,3]] and v[1] is the column vector [0,1]. The characteristic polynomial of the matrix M is x^2-3x-3.
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LINKS
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Index entries for sequences related to linear recurrences with constant coefficients
Tanya Khovanova, Recursive Sequences
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FORMULA
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a(n)=(1/7)*[3/2+(1/2)*sqrt(21)]^n*sqrt(21)-(1/7)*sqrt(21)*[3/2-(1/2)*sqrt(21)]^n, with n>=0 [From Paolo P. Lava (ppl(AT)spl.at), Aug 01 2008]
G.f.: 3x/(1-3x-3x^2). [From Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Nov 19 2008]
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PROGRAM
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(PARI) a(n)=([0, 3; 1, 3]^n)[1, 2]
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CROSSREFS
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Equals 3*A030195(n). Cf. A028860.
Sequence in context: A125792 A149020 A057390 this_sequence A058540 A156016 A032314
Adjacent sequences: A106432 A106433 A106434 this_sequence A106436 A106437 A106438
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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 29 2005
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EXTENSIONS
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Edited by N. J. A. Sloane (njas(AT)research.att.com), May 20 2006 and May 29 2006
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