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A150994 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, 0, 0), (0, -1, 1), (1, 0, -1), (1, 1, 0), (1, 1, 1)} 0
1, 2, 9, 38, 170, 788, 3701, 17621, 84743, 409854, 1993846, 9739235, 47723741, 234520717, 1154955011, 5698424753, 28160079693, 139341098410, 690273126559, 3422846851125, 16987118264372, 84367242024066, 419283901941142, 2084919612584816, 10372633738439073, 51627625733592623, 257067798731839391 (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, k, -1 + n] + aux[-1 + i, j, 1 + k, -1 + n] + aux[i, 1 + j, -1 + k, -1 + n] + aux[1 + i, 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: A291462 A001077 A150993 * A150995 A150996 A150997

Adjacent sequences:  A150991 A150992 A150993 * A150995 A150996 A150997

KEYWORD

nonn,walk

AUTHOR

Manuel Kauers, Nov 18 2008

STATUS

approved

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Last modified February 23 13:05 EST 2018. Contains 299581 sequences. (Running on oeis4.)