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Search: id:A145602
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| A145602 |
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a(n) is the number of walks from (0,0) to (0,3) that remain in the upper half-plane y >= 0 using 2*n +1 unit steps either up (U), down (D), left (L) or right (R). |
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+0
6
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| 1, 24, 392, 5760, 81675, 1145144, 16032016, 225059328, 3173688180, 44986664800, 641087516256, 9183622822400, 132211882468575, 1912322889603000, 27781440618420000, 405248874740582400, 5933888308457316900
(list; graph; listen)
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OFFSET
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1,2
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COMMENT
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Cf. A000891, which enumerates walks in the upper half-plane starting and finishing at the origin. See also A145600, A145601 and A145603. This sequence is the central column taken from the triangle A145598, which enumerates walks in the upper half-plane starting at the origin and finishing on the horizontal line y = 3.
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LINKS
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R. K. Guy, Catwalks, sandsteps and Pascal pyramids, J. Integer Sequences, Vol. 3 (2000), Article #00.1.6
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FORMULA
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a(n) = 2/(n+1)*binomial(2*n+2,n+3)*binomial(2*n+2,n-1).
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MAPLE
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with(combinat):
a(n) = 2/(n+1)*binomial(2*n+2, n+3)*binomial(2*n+2, n-1);
seq(a(n), n = 1..19);
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CROSSREFS
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A000891, A145598, A145600, A145601, A145603.
Sequence in context: A022448 A025947 A007752 this_sequence A020447 A021894 A021694
Adjacent sequences: A145599 A145600 A145601 this_sequence A145603 A145604 A145605
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KEYWORD
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easy,nonn
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AUTHOR
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Peter Bala (pbala(AT)toucansurf.com), Oct 15 2008
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