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Search: id:A135390
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| A135390 |
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Number of walks from origin to (1,0,0) in a cubic lattice. |
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+0
1
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| 1, 15, 310, 7455, 195426, 5416026, 156061620, 4628393055, 140348412490, 4331544836190, 135614951248140, 4296741195214650, 137507314754659500, 4438467396322843500, 144329729055650881560, 4723733064176346346335
(list; graph; listen)
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OFFSET
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0,2
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COMMENT
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a(n) is the number of walks of length 2n+1 on a cubic lattice that start at the origin and end at (1,0,0) using steps (1,0,0), (-1,0,0), (0,1,0), (0,-1,0), (0,0,1), (0,0,-1).
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LINKS
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S. Hollos and R. Hollos, Lattice Paths and Walks.
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FORMULA
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a(n) = binomial(2n+1,n) * sum( binomial(n,k) * binomial(n+1,k) * binomial(2k,k), k, 0, n )
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PROGRAM
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Maxima: a(n) = binomial(2n+1, n) * sum( binomial(n, k) * binomial(n+1, k) * binomial(2k, k), k, 0, n )
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CROSSREFS
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Cf. A002896.
Adjacent sequences: A135387 A135388 A135389 this_sequence A135391 A135392 A135393
Sequence in context: A009064 A049381 A051691 this_sequence A105491 A133766 A112489
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KEYWORD
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easy,nonn
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AUTHOR
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Stefan Hollos (stefan(AT)exstrom.com), Dec 11 2007
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