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A081575
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Fifth binomial transform of Fibonacci numbers F(n).
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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; refs; listen; history; internal format)
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OFFSET
| 0,3
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COMMENTS
| 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
| 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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MATHEMATICA
| Join[{a=0, b=1}, Table[c=11*b-29*a; a=b; b=c, {n, 60}]] (*From Vladimir Joseph Stephan Orlovsky, Jan 31 2011*)
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PROG
| (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
| Cf. A000045, A081570.
Sequence in context: A044262 A044643 A025507 * A016150 A115203 A164547
Adjacent sequences: A081572 A081573 A081574 * A081576 A081577 A081578
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KEYWORD
| easy,nonn
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AUTHOR
| Paul Barry (pbarry(AT)wit.ie), Mar 24 2003
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