|
Search: id:A015445
|
|
|
| A015445 |
|
Generalized Fibonacci numbers: a(n) = a(n-1) + 9 a(n-2). |
|
+0
7
|
|
| 1, 1, 10, 19, 109, 280, 1261, 3781, 15130, 49159, 185329, 627760, 2295721, 7945561, 28607050, 100117099, 357580549, 1258634440, 4476859381, 15804569341, 56096303770, 198337427839, 703204161769, 2488241012320
(list; graph; listen)
|
|
|
OFFSET
|
0,3
|
|
|
FORMULA
|
a(n)={[ (1+sqrt(37))/2 ]^(n+1) - [ (1-sqrt(37))/2 ]^(n+1)}/sqrt(37).
a(n)=sum{k=0..floor(n/2), binomial(n-k, k)9^k } - Paul Barry (pbarry(AT)wit.ie), Jul 20 2004
a(n)=sum{k=0..n, binomial((n+k)/2, (n-k)/2)(1+(-1)^(n-k))3^(n-k)/2}; - Paul Barry (pbarry(AT)wit.ie), Aug 28 2005
a(n)=Sum_{k, 0<=k<=n} A109466(n,k)*(-9)^(n-k). [From Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Oct 26 2008]
|
|
PROGRAM
|
(Other) sage: [lucas_number1(n, 1, -9) for n in xrange(1, 25)] # [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Apr 22 2009]
|
|
CROSSREFS
|
Cf. A015443, A015442.
Adjacent sequences: A015442 A015443 A015444 this_sequence A015446 A015447 A015448
Sequence in context: A131495 A060630 A070199 this_sequence A123001 A073222 A110463
|
|
KEYWORD
|
nonn,easy
|
|
AUTHOR
|
Olivier Gerard (olivier.gerard(AT)gmail.com)
|
|
|
Search completed in 0.002 seconds
|
