|
Search: id:A015454
|
|
|
| A015454 |
|
Generalized Fibonacci numbers. |
|
+0
3
|
|
| 1, 1, 9, 73, 593, 4817, 39129, 317849, 2581921, 20973217, 170367657, 1383914473, 11241683441, 91317382001, 741780739449, 6025563297593, 48946287120193, 397595860259137, 3229713169193289, 26235301213805449
(list; graph; listen)
|
|
|
OFFSET
|
0,3
|
|
|
COMMENT
|
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
|
|
LINKS
|
Index entries for sequences related to linear recurrences with constant coefficients
Tanya Khovanova, Recursive Sequences
|
|
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 (ppl(AT)spl.at), Nov 21 2008]
|
|
CROSSREFS
|
Sequence in context: A081627 A164588 A023001 this_sequence A121246 A086226 A015465
Adjacent sequences: A015451 A015452 A015453 this_sequence A015455 A015456 A015457
|
|
KEYWORD
|
nonn,easy
|
|
AUTHOR
|
Olivier Gerard (olivier.gerard(AT)gmail.com)
|
|
|
Search completed in 0.002 seconds
|
