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A081569
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Fourth binomial transform of F(n+1).
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5
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1, 5, 26, 139, 757, 4172, 23165, 129217, 722818, 4050239, 22718609, 127512940, 715962889, 4020920141, 22584986378, 126867394723, 712691811325, 4003745802188, 22492567804517, 126361939999081, 709898671705906
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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COMMENTS
| Binomial transform of A081568 Case k=4 of family of recurrences a(n)=(2k+1)a(n-1)-A028387(k-1)a(n-2),a(0)=1,a(1)=k+1.
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FORMULA
| a(n)=9a(n-1)-19a(n-2), a(0)=1, a(1)=5. a(n)=(1/2 - sqrt(5)/10)(9/2 - sqrt(5)/2)^n + (sqrt(5)/10 + 1/2)(sqrt(5)/2 + 9/2)^n G.f.: (1-4x)/(1-9x+19x^2).
a(n)= Sum_{k, 0<=k<=n} A094441(n,k)*4^k. [From Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Dec 14 2009]
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CROSSREFS
| Cf. A000045.
Sequence in context: A161731 A049607 A035029 * A005573 A081911 A081187
Adjacent sequences: A081566 A081567 A081568 * A081570 A081571 A081572
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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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