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A015449
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Generalized Fibonacci numbers.
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8
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1, 1, 6, 31, 161, 836, 4341, 22541, 117046, 607771, 3155901, 16387276, 85092281, 441848681, 2294335686, 11913527111, 61861971241, 321223383316, 1667978887821, 8661117822421, 44973567999926, 233528957822051
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,3
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LINKS
| Index entries for sequences related to linear recurrences with constant coefficients
Joerg Arndt, Fxtbook
Tanya Khovanova, Recursive Sequences
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FORMULA
| a(n) = 5 a(n-1) + a(n-2).
a(n)=Sum_{k, 0<=k<=n}4^k*A055830(n,k) . - Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Oct 18 2006
G.f.: (1-4*x)/(1-5*x-x^2). [From Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Nov 20 2008]
a(n)=(1/2)*[(5/2)+(1/2)*sqrt(29)]^n-(3/58)*[(5/2)+(1/2)*sqrt(29)]^n*sqrt(29)+(1/2)*[(5/2)-(1/2) *sqrt(29)]^n+(3/58)*sqrt(29)*[(5/2)-(1/2)*sqrt(29)]^n, with n>=0 [From Paolo P. Lava (paoloplava(AT)gmail.com), Nov 21 2008]
Contribution from Johannes W. Meijer (meijgia(AT)hotmail.com), Aug 01 2010: (Start)
Binomial transform of A152187.
(End)
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MAPLE
| a[0]:=1: a[1]:=1: for n from 2 to 26 do a[n]:=5*a[n-1]+a[n-2] od: seq(a[n], n=0..21); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Jul 26 2006
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MATHEMATICA
| Transpose[NestList[Flatten[{Rest[#], ListCorrelate[{1, 5}, #]}]&, {1, 1}, 40]][[1]] (* From Harvey P. Dale, Mar 23 2011 *)
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CROSSREFS
| Sequence in context: A047665 A003128 A058146 * A162475 A036729 A199320
Adjacent sequences: A015446 A015447 A015448 * A015450 A015451 A015452
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KEYWORD
| nonn,easy
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AUTHOR
| Olivier Gerard (olivier.gerard(AT)gmail.com)
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