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A099100
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Fibonacci(5n+1).
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10
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1, 8, 89, 987, 10946, 121393, 1346269, 14930352, 165580141, 1836311903, 20365011074, 225851433717, 2504730781961, 27777890035288, 308061521170129, 3416454622906707, 37889062373143906, 420196140727489673, 4660046610375530309, 51680708854858323072, 573147844013817084101, 6356306993006846248183
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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LINKS
| Tanya Khovanova, Recursive Sequences
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FORMULA
| G.f.: (1-3x)/(1-11x-x^2); a(n)=11a(n-1)+a(n-2); a(n)=sum{k=0..5n, binomial(k, 5n-k)}.
a(n)=-(1/10)*[(11/2)-(5/2)*sqrt(5)]^n*sqrt(5)+(1/2)*[(11/2)-(5/2)*sqrt(5)]^n+(1/10)*sqrt(5)*[(11/2)+(5 /2)*sqrt(5)]^n+(1/2)*[(11/2)+(5/2)*sqrt(5)]^n, with n>=0 [From Paolo P. Lava (paoloplava(AT)gmail.com), Nov 19 2008]
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MATHEMATICA
| Fibonacci/@(5*Range[0, 30]+1) [From Vladimir Orlovsky (4vladimir(AT)gmail.com), Mar 01 2010]
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PROG
| (MAGMA) [Fibonacci(5*n+1): n in [0..100]]; // Vincenzo Librandi, Apr 16 2011
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CROSSREFS
| Cf. A000045.
Sequence in context: A068498 A061000 A072352 * A184756 A131655 A105718
Adjacent sequences: A099097 A099098 A099099 * A099101 A099102 A099103
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KEYWORD
| easy,nonn
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AUTHOR
| Paul Barry (pbarry(AT)wit.ie), Sep 29 2004
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EXTENSIONS
| Corrected second formula. - Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Nov 16 2008
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