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A025276
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a(n) = a(1)*a(n-1) + a(2)*a(n-2) + ...+ a(n-1)*a(1) for n >= 5.
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2
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1, 0, 0, 1, 2, 4, 8, 17, 38, 88, 208, 498, 1204, 2936, 7216, 17861, 44486, 111408, 280352, 708526, 1797564, 4576472, 11688496, 29939786, 76894684, 197974480, 510864480, 1321031716, 3422685992, 8884010928, 23098674400, 60152509613, 156879556678
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,5
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COMMENTS
| Number of lattice paths from (0,0) to (n-4,0) that stay weakly in the first quadrant and such that each step is either U=(2,1), D=(2,-1), blue H=(1,0), or red h=(1,0) (n>=4). E.g. a(8)=17 because we have 16 horizontal paths of length 4 with all combinations of blue and red (1,0) steps and, in addition, UD. - Emeric Deutsch (deutsch(AT)duke.poly.edu), Dec 23 2003
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LINKS
| Reinhard Zumkeller, Table of n, a(n) for n = 1..1000
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FORMULA
| G.f.=[1-sqrt((1-2z)^2-4z^4)]/2. - Emeric Deutsch (deutsch(AT)duke.poly.edu), Dec 23 2003
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PROG
| (Haskell)
a025276 n = a025276_list !! (n-1)
a025276_list = 1 : 0 : 0 : 1 : f [1, 0, 0, 1] where
f xs = x' : f (x':xs) where
x' = sum $ zipWith (*) xs a025276_list
-- Reinhard Zumkeller, Nov 03 2011
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CROSSREFS
| Sequence in context: A082499 A100131 A119685 * A006461 A003007 A086615
Adjacent sequences: A025273 A025274 A025275 * A025277 A025278 A025279
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KEYWORD
| nonn
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AUTHOR
| Clark Kimberling (ck6(AT)evansville.edu)
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