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A015454
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Generalized Fibonacci numbers.
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3
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1, 1, 9, 73, 593, 4817, 39129, 317849, 2581921, 20973217, 170367657, 1383914473, 11241683441, 91317382001, 741780739449, 6025563297593, 48946287120193, 397595860259137, 3229713169193289, 26235301213805449
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,3
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COMMENTS
| a(n)/a(n-1) tends to (8 + 2*sqrt(17))/2 = exp ArcSinh 4. - Gary W. Adamson (qntmpkt(AT)yahoo.com), Dec 26 2007
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LINKS
| Index entries for sequences related to linear recurrences with constant coefficients
Tanya Khovanova, Recursive Sequences
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FORMULA
| a(n) = 8 a(n-1) + a(n-2).
a(n)=Sum_{k, 0<=k<=n}7^k*A055830(n,k) . - Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Oct 18 2006
G.f.: (1-7*x)/(1-8*x-x^2). [From Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Nov 20 2008]
a(n)=(3/34)*sqrt(17)*[4-sqrt(17)]^n-(3/34)*[4+sqrt(17)]^n*sqrt(17)+(1/2)*[4+sqrt(17)]^n+(1/2) *[4-sqrt(17)]^n, with n>=0 [From Paolo P. Lava (paoloplava(AT)gmail.com), Nov 21 2008]
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CROSSREFS
| Sequence in context: A081627 A164588 A023001 * A121246 A086226 A199677
Adjacent sequences: A015451 A015452 A015453 * A015455 A015456 A015457
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KEYWORD
| nonn,easy
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AUTHOR
| Olivier Gerard (olivier.gerard(AT)gmail.com)
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