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Search: id:A015447
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| A015447 |
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Generalized Fibonacci numbers: a(n) = a(n-1) + 11 a(n-2). |
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+0
6
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| 1, 1, 12, 23, 155, 408, 2113, 6601, 29844, 102455, 430739, 1557744, 6295873, 23431057, 92685660, 350427287, 1369969547, 5224669704, 20294334721, 77765701465, 301003383396, 1156426099511, 4467463316867, 17188150411488
(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+3*sqrt(5))/2 ]^(n+1) - [ (1-3*sqrt(5))/2 ]^(n+1)}/3*sqrt(5).
a(n-1)=(1/3)*(-1)^n*sum(i=0, n, (-3)^i*F(i)*C(n, i)) - Benoit Cloitre (benoit7848c(AT)orange.fr), Mar 06 2004
a(n)=Sum_{k, 0<=k<=n} A109466(n,k)*(-11)^(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, -11) for n in xrange(0, 27)] # [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Apr 22 2009]
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CROSSREFS
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Cf. A015446, A015443.
Sequence in context: A049852 A045532 A083683 this_sequence A072822 A059161 A133491
Adjacent sequences: A015444 A015445 A015446 this_sequence A015448 A015449 A015450
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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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