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A081574
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Fourth binomial transform of Fibonacci numbers F(n).
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4
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0, 1, 9, 62, 387, 2305, 13392, 76733, 436149, 2467414, 13919895, 78398189, 441105696, 2480385673, 13942462833, 78354837710, 440286745563, 2473838793577, 13899100976496, 78088971710501, 438717826841085
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,3
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COMMENTS
| Binomial transform of A099453(n-1):= [0,1,7,38,189,905,...]. Case k=4 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)=9a(n-1)-19a(n-1), a(0)=0, a(1)=1. a(n)=((sqrt(5)/2+9/2)^n-(9/2-sqrt(5)/2)^n)/sqrt(5). G.f.: x/(1-9x+19x^2).
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MATHEMATICA
| Join[{a=0, b=1}, Table[c=9*b-19*a; a=b; b=c, {n, 60}]] (*From Vladimir Joseph Stephan Orlovsky, Jan 27 2011*)
LinearRecurrence[{9, -19}, {0, 1}, 30] (* From Harvey P. Dale, Dec 03 2011 *)
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PROG
| (Other) sage: [lucas_number1(n, 9, 19) for n in xrange(0, 21)]# [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Apr 23 2009]
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CROSSREFS
| Cf. A000045, A081569.
Sequence in context: A075139 A098921 A027234 * A084151 A159235 A181403
Adjacent sequences: A081571 A081572 A081573 * A081575 A081576 A081577
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KEYWORD
| easy,nonn
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AUTHOR
| Paul Barry (pbarry(AT)wit.ie), Mar 22 2003
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EXTENSIONS
| Corrected by Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Dec 16 2009
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