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Search: id:A108447
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| A108447 |
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Number of paths from (0,0) to (3n,0) that stay in the first quadrant (but may touch the horizontal axis), consisting of steps u=(2,1),U=(1,2), or d=(1,-1), and have no peaks of the form ud. |
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+0
6
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| 1, 1, 4, 20, 113, 688, 4404, 29219, 199140, 1385904, 9807820, 70364704, 510609620, 3741212535, 27639233548, 205660399220, 1539916433473, 11594310041792, 87725707127600, 666681174728724, 5086601816592432, 38948589882247968
(list; graph; listen)
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OFFSET
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0,3
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COMMENT
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Column 0 of A108446.
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REFERENCES
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Problem 10658, American Math. Monthly, 107, 2000, 368-370.
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FORMULA
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a(n)=(1/n)sum(binomial(n, j)*binomial(n+2j, j-1), j=0..n) (n>=1); a(0)=1. G.f.=G satisfies G=1+zG(G^2+G-1).
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EXAMPLE
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a(2)=4 because we have uUddd, UddUdd, UdUddd, and UUdddd.
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MAPLE
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a:=n->(1/n)*sum(binomial(n, j)*binomial(n+2*j, j-1), j=0..n): 1, seq(a(n), n=1..25);
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CROSSREFS
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Cf. A027307, A108446, A108425, A108426.
Sequence in context: A080609 A003645 A081085 this_sequence A028475 A128327 A100034
Adjacent sequences: A108444 A108445 A108446 this_sequence A108448 A108449 A108450
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KEYWORD
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nonn
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AUTHOR
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Emeric Deutsch (deutsch(AT)duke.poly.edu), Jun 10 2005
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