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Search: id:A015446
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| A015446 |
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Generalized Fibonacci numbers: a(n) = a(n-1) + 10 a(n-2). |
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+0
7
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| 1, 1, 11, 21, 131, 341, 1651, 5061, 21571, 72181, 287891, 1009701, 3888611, 13985621, 52871731, 192727941, 721445251, 2648724661, 9863177171, 36350423781, 134982195491, 498486433301, 1848308388211, 6833172721221
(list; graph; listen)
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OFFSET
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0,3
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FORMULA
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a(n)={[ (1+sqrt(41))/2 ]^(n+1) - [ (1-sqrt(41))/2 ]^(n+1)}/sqrt(41).
a(n)=sum{k=0..n, binomial((n+k)/2, k)(1+(-1)^(n-k))10^((n-k)/2)/2}; a(n)=sum{k=0..floor(n/2), binomial(n-k, k)10^k}; - Paul Barry (pbarry(AT)wit.ie), Sep 10 2005
a(n) is the entry (M^n)_1,1 where the matrix M = [1,2;5,0]. - Simone Severini (ss54(AT)york.ac.uk), Jun 22 2006
a(n)=Sum_{k, 0<=k<=n} A109466(n,k)*(-10)^(n-k). [From Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Oct 26 2008]
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PROGRAM
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(Other) sage: [lucas_number1(n, 1, -10) for n in xrange(1, 25)] # [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Apr 22 2009]
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CROSSREFS
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Cf. A015447, A015443.
Sequence in context: A116525 A094623 A034922 this_sequence A083177 A110466 A110383
Adjacent sequences: A015443 A015444 A015445 this_sequence A015447 A015448 A015449
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KEYWORD
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nonn,easy
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AUTHOR
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Olivier Gerard (olivier.gerard(AT)gmail.com)
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