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Search: id:A081575
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| A081575 |
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Fifth binomial transform of Fibonacci numbers F(n). |
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+0
2
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| 0, 1, 11, 92, 693, 4955, 34408, 234793, 1584891, 10624804, 70911005, 471901739, 3134499984, 20794349393, 137837343787, 913174649260, 6047638172037, 40041955063867, 265079998713464, 1754663288995961, 11613976216265115
(list; graph; listen)
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OFFSET
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0,3
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COMMENT
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Binomial transform of A081574. Case k=5 of family of recurrences a(n)=(2k+1)a(n-1)-A028387(k-1)a(n-2),a(0)=0,a(1)=1.
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FORMULA
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a(n)=11a(n-1)-29a(n-2), a(0)=0, a(1)=1. a(n)=((sqrt(5)/2+11/2)^n-(11/2-sqrt(5)/2)^n)/sqrt(5) G.f. 1/(1-11x+29x^2).
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PROGRAM
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(Other) sage: [lucas_number1(n, 11, 29) for n in xrange(0, 21)]# [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Apr 27 2009]
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CROSSREFS
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Cf. A000045, A081570.
Sequence in context: A044262 A044643 A025507 this_sequence A016150 A115203 A164547
Adjacent sequences: A081572 A081573 A081574 this_sequence A081576 A081577 A081578
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KEYWORD
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easy,nonn
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AUTHOR
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Paul Barry (pbarry(AT)wit.ie), Mar 24 2003
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