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 A101890 Sum C(n,2k)F(k), k=0..floor(n/2). 1
 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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,4 COMMENTS 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 LINKS Index to sequences with linear recurrences with constant coefficients, signature (4,-5,2,1). FORMULA 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}. CROSSREFS Cf. A000045. Sequence in context: A099444 A132402 A137166 * A134195 A079444 A146654 Adjacent sequences:  A101887 A101888 A101889 * A101891 A101892 A101893 KEYWORD easy,nonn AUTHOR Paul Barry, Dec 20 2004 STATUS approved

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