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A100095
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An inverse Chebyshev transform of the Fibonacci numbers.
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3
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0, 1, 1, 5, 7, 25, 41, 125, 225, 625, 1195, 3125, 6227, 15625, 32059, 78125, 163727, 390625, 831505, 1953125, 4206145, 9765625, 21215481, 48828125, 106782837, 244140625, 536618341, 1220703125, 2693492305, 6103515625, 13507578125
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,4
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COMMENTS
| Image of x/(1-x-x^2) under the transform g(x)->(1/sqrt(1-4xx^2)g(xc(x^2)), where c(x) is the g.f. of the Catalan numbers A000108. This is the inverse of the Chebyshev transform which takes A(x) to ((1-x^2)/(1+x^2))A(x/(1+x^2)).
Hankel transform is (-1)^n*(2^n-0^n)/2. Hankel transform of a(n+1) is A141125. - Paul Barry (pbarry(AT)wit.ie), Jun 05 2008
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FORMULA
| G.f.: (x^2*sqrt(1-4x^2)+x*(1-4x^2))/((1-4x^2)(1-5x^2)); a(n)=sum{k=0..floor(n/2), binomial(n, k)Fib(n-2k)}.
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CROSSREFS
| Cf. A000045, A100096, A100097.
Sequence in context: A003595 A018697 A018319 * A179782 A013626 A067701
Adjacent sequences: A100092 A100093 A100094 * A100096 A100097 A100098
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KEYWORD
| easy,nonn
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AUTHOR
| Paul Barry (pbarry(AT)wit.ie), Nov 03 2004
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