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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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10
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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; refs; listen; history; internal format)
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OFFSET
| 0,2
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COMMENTS
| 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
| Reinhard Zumkeller, Table of n, a(n) for n = 0..1000
Tanya Khovanova, Recursive Sequences
Index entries for sequences related to linear recurrences with constant coefficients
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FORMULA
| 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 (paoloplava(AT)gmail.com), Aug 01 2008]
G.f.: 3x/(1-3x-3x^2). [From Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Nov 19 2008]
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PROG
| (PARI) a(n)=([0, 3; 1, 3]^n)[1, 2]
(Haskell)
a106435 n = a106435_list !! n
a106435_list = 0 : 3 : map (* 3) (zipWith (+) a106435_list (tail
a106435_list))
-- Reinhard Zumkeller, Oct 15 2011
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CROSSREFS
| Equals 3*A030195(n). Cf. A028860.
A002605, A026150, A028859, A080040, A083337, A108898, A125145.
Sequence in context: A057390 A183495 A185162 * A058540 A156016 A032314
Adjacent sequences: A106432 A106433 A106434 * A106436 A106437 A106438
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KEYWORD
| nonn,easy
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AUTHOR
| Roger L. Bagula (rlbagulatftn(AT)yahoo.com), May 29 2005
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EXTENSIONS
| Edited by N. J. A. Sloane (njas(AT)research.att.com), May 20 2006 and May 29 2006
Offset corrected by Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Oct 15 2011
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