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Search: id:A015451
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| A015451 |
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a(n) = 6 a(n-1) + a(n-2). |
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+0
3
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| 1, 1, 7, 43, 265, 1633, 10063, 62011, 382129, 2354785, 14510839, 89419819, 551029753, 3395598337, 20924619775, 128943316987, 794584521697, 4896450447169, 30173287204711, 185936173675435, 1145790329257321
(list; graph; listen)
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OFFSET
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0,3
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COMMENT
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a(n) = term (1,1) in the 2x2 matrix [1,2; 3,5]^n. - Gary W. Adamson (qntmpkt(AT)yahoo.com), May 30 2008
a(n)/a(n-1) tends to sqrt(10 + 3 = 6.16227766... - Gary W. Adamson (qntmpkt(AT)yahoo.com), May 30 2008
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LINKS
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Tanya Khovanova, Recursive Sequences
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FORMULA
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a(n)=Sum_{k, 0<=k<=n}5^k*A055830(n,k) . - Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Oct 18 2006
a(n)=(1/10)*[3-sqrt(10)]^n*sqrt(10)-(1/10)*[3+sqrt(10)]^n*sqrt(10)+(1/2)*[3+sqrt(10)]^n+(1/2) *[3-sqrt(10)]^n, with n>=0 - Paolo P. Lava (ppl(AT)spl.at), Jun 25 2008
G.f.: (1-5*x)/(1-6*x-x^2). [From Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Nov 20 2008]
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MAPLE
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a[0]:=1: a[1]:=1: for n from 2 to 26 do a[n]:=6*a[n-1]+a[n-2] od: seq(a[n], n=0..20); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Jul 26 2006
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CROSSREFS
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Sequence in context: A161728 A003464 A022036 this_sequence A126502 A042213 A164775
Adjacent sequences: A015448 A015449 A015450 this_sequence A015452 A015453 A015454
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KEYWORD
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nonn,easy
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AUTHOR
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Olivier Gerard (olivier.gerard(AT)gmail.com)
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