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A074677
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a(n)=Sum((-1)^(i+Floor(n/2))F(2i+e),(i=0,..,Floor(n/2))), where F(n) = Fibonacci numbers and e=(1/2)(1-(-1)^n).
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5
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0, 1, 1, 1, 2, 4, 6, 9, 15, 25, 40, 64, 104, 169, 273, 441, 714, 1156, 1870, 3025, 4895, 7921, 12816, 20736, 33552, 54289, 87841, 142129, 229970, 372100, 602070, 974169, 1576239, 2550409, 4126648, 6677056, 10803704, 17480761, 28284465, 45765225
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,5
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COMMENTS
| Essentially the same as A006498 (g.f. 1/(1-x-x^3-x^4)).
a(n) is the convolution of F(n) with the sequence (1,0,-1,0,1,0,-1,0,...), A056594.
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LINKS
| Reinhard Zumkeller, Table of n, a(n) for n = 0..1000
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FORMULA
| a(n)=a(n-1)+a(n-3)+a(n-4), a(0)=0, a(1)=1, a(2)=1, a(3)=1.
G.f.: x/(1 - x - x^3 - x^4).
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MATHEMATICA
| CoefficientList[Series[x/(1 - x - x^3 - x^4), {x, 0, 40}], x]
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PROG
| (Haskell)
a074677 n = a074677_list !! (n-1)
a074677_list = 0 : 1 : 1 : 1 : zipWith (+) a074677_list
(zipWith (+) (tail a074677_list) (drop 3 a074677_list))
-- Reinhard Zumkeller, Dec 28 2011
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CROSSREFS
| Cf. A056594.
Sequence in context: A057602 A171646 A006498 * A179997 A101756 A173241
Adjacent sequences: A074674 A074675 A074676 * A074678 A074679 A074680
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KEYWORD
| easy,nonn
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AUTHOR
| Mario Catalani (mario.catalani(AT)unito.it), Aug 30 2002
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