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A150630 Number of walks within N^3 (the first octant of Z^3) starting at (0,0,0) and consisting of n steps taken from {(-1, -1, 0), (-1, -1, 1), (0, 1, 0), (1, 1, -1), (1, 1, 1)} 0
1, 2, 7, 27, 115, 496, 2203, 9920, 45411, 209940, 979623, 4601579, 21744703, 103247146, 492314131, 2355900011, 11309419723, 54439264932, 262687966031, 1270289989275, 6154650238423, 29871399257282, 145206884273859, 706861991466206, 3445426296696735, 16813717974366998, 82139970279742863 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

LINKS

Table of n, a(n) for n=0..26.

A. Bostan and M. Kauers, 2008. Automatic Classification of Restricted Lattice Walks, ArXiv 0811.2899.

MATHEMATICA

aux[i_Integer, j_Integer, k_Integer, n_Integer] := Which[Min[i, j, k, n] < 0 || Max[i, j, k] > n, 0, n == 0, KroneckerDelta[i, j, k, n], True, aux[i, j, k, n] = aux[-1 + i, -1 + j, -1 + k, -1 + n] + aux[-1 + i, -1 + j, 1 + k, -1 + n] + aux[i, -1 + j, k, -1 + n] + aux[1 + i, 1 + j, -1 + k, -1 + n] + aux[1 + i, 1 + j, k, -1 + n]]; Table[Sum[aux[i, j, k, n], {i, 0, n}, {j, 0, n}, {k, 0, n}], {n, 0, 10}]

CROSSREFS

Sequence in context: A154108 A011965 A150629 * A150631 A150632 A150633

Adjacent sequences:  A150627 A150628 A150629 * A150631 A150632 A150633

KEYWORD

nonn,walk

AUTHOR

Manuel Kauers, Nov 18 2008

STATUS

approved

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Last modified April 24 13:01 EDT 2014. Contains 240983 sequences.