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Search: id:A101891
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| A101891 |
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Sum C(n,2k)F(k+1), k=0..floor(n/2). |
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+0
1
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| 1, 1, 2, 4, 9, 21, 49, 113, 258, 586, 1329, 3015, 6845, 15549, 35330, 80280, 182413, 414461, 941669, 2139477, 4860898, 11044006, 25092157, 57009871, 129527609, 294289401, 668631458, 1519143916, 3451524785, 7841931877, 17817022873
(list; graph; listen)
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OFFSET
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0,3
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COMMENT
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Transform of F(n+1) under the mapping g(x)-> (1/(1-x))g(x^2/((1-x)^2). Binomial transform of 1,0,1,0,2,0,3,0,5,...
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FORMULA
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G.f.: (1-x)^3/(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)/2)(1+(-1)^k)/2}.
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CROSSREFS
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Cf. A000045.
Adjacent sequences: A101888 A101889 A101890 this_sequence A101892 A101893 A101894
Sequence in context: A084634 A137256 A051164 this_sequence A119967 A052921 A018905
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KEYWORD
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easy,nonn
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AUTHOR
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Paul Barry (pbarry(AT)wit.ie), Dec 20 2004
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