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A101890
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Sum C(n,2k)F(k), k=0..floor(n/2).
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1
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0, 0, 1, 3, 7, 15, 32, 70, 157, 357, 815, 1859, 4232, 9620, 21853, 49635, 112747, 256139, 581944, 1322210, 3004145, 6825557, 15507867, 35234183, 80052656, 181881000, 413236953, 938882307, 2133159119, 4846579847, 11011525360
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OFFSET
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0,4
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COMMENTS
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Transform of F(n) under the mapping g(x)-> (1/(1-x))g(x^2/((1-x)^2). Binomial transform of aerated Fibonacci numbers 0,0,1,0,1,0,2,0,3,0,5,...
F(n) may be recovered as sum{k=0..2n, sum{j=0..k,C(0,2n-k)C(k,j)(-1)^(k-j)*A101890(j)}}. - Paul Barry, Jun 10 2005
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LINKS
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Table of n, a(n) for n=0..30.
Index to sequences with linear recurrences with constant coefficients, signature (4,-5,2,1).
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FORMULA
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G.f.: x^2(1-x)/(1-4x+5x^2-2x^3-x^4); a(n)=4a(n-1)-5a(n-2)+2a(n-3)+a(n-4); a(n)=sum{k=0..n, binomial(n, k)(F(k/2)(1+(-1)^k)/2}.
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CROSSREFS
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Cf. A000045.
Sequence in context: A099444 A132402 A137166 * A134195 A079444 A146654
Adjacent sequences: A101887 A101888 A101889 * A101891 A101892 A101893
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KEYWORD
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easy,nonn
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AUTHOR
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Paul Barry, Dec 20 2004
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STATUS
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approved
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