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Search: id:A033887
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| 1, 3, 13, 55, 233, 987, 4181, 17711, 75025, 317811, 1346269, 5702887, 24157817, 102334155, 433494437, 1836311903, 7778742049, 32951280099, 139583862445, 591286729879, 2504730781961, 10610209857723
(list; graph; listen)
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OFFSET
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0,2
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COMMENT
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Second binomial transform of (1,1,5,5,25,25,....). - Paul Barry (pbarry(AT)wit.ie), Jul 16 2003
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LINKS
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Tanya Khovanova, Recursive Sequences
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FORMULA
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a(n) = 4a(n-1)+a(n-2), n>1, a(0)=1, a(1)=3; G.f.: (1-x)/(1-4*x-x^2); a(n)=[ (1+sqrt(5))(2+sqrt(5))^n - (1-sqrt(5))(2-sqrt(5))^n ]/2*sqrt(5).
a(n)=sum{k=0..n, sum{j=0..n-k, C(n,j)C(n-j,k)F(n-j+1)}}; - Paul Barry (pbarry(AT)wit.ie), May 19 2006
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MAPLE
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with(combinat): a:=n->fibonacci(n, 4)-fibonacci(n-1, 4): seq(a(n), n=1..22); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Apr 04 2008
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CROSSREFS
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A033887(n)=A001076(n)+A001077(n).
Equals 2*A049651(n) + 1.
Sequence in context: A140320 A037583 A093834 this_sequence A117376 A102287 A006225
Adjacent sequences: A033884 A033885 A033886 this_sequence A033888 A033889 A033890
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KEYWORD
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nonn,easy
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AUTHOR
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njas
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