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Search: id:A108081
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| A108081 |
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Sum [i=0..n, C(2n-i,n+i) ]. |
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2
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| 1, 2, 7, 25, 92, 344, 1300, 4950, 18955, 72905, 281403, 1089343, 4227273, 16438345, 64037453, 249855417, 976205516, 3818779616, 14954876080, 58623077586, 230007291334, 903164858092, 3549071519462, 13955918890440
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OFFSET
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0,2
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COMMENT
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A transform of the Fibonacci numbers A000045(n+1) under the mapping g(x)->(1/(c(x)sqrt(1-4x))g(xc(x)), c(x) the g.f. of A000108. Hankel transform is the bisection of the Fibonacci numbers F(2n+2) (A001906(n+1)). - Paul Barry (pbarry(AT)wit.ie), Sep 28 2007
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FORMULA
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G.f.: 1/2*(1-5*x+4*x^2+((1-4*x)*(1-5*x)^2)^(1/2))/(1-4*x)/(1-4*x-x^2). - Vladeta Jovovic (vladeta(AT)Eunet.yu), Sep 06 2006
G.f.: (1+sqrt(1-4x))/(2*sqrt(1-4x)*(x+sqrt(1-4x))); - Paul Barry (pbarry(AT)wit.ie), Sep 28 2007
a(n)=sum{k=0..n, C(n+k-1,k)F(n-k+1)}; - Paul Barry (pbarry(AT)wit.ie), Sep 28 2007
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CROSSREFS
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Sequence in context: A097613 A024482 A074605 this_sequence A116396 A074421 A036784
Adjacent sequences: A108078 A108079 A108080 this_sequence A108082 A108083 A108084
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KEYWORD
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nonn
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AUTHOR
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Ralf Stephan, Jun 03 2005
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