A150104 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, 0), (0, 0, 1), (0, 1, 1), (1, 0, -1)}.

1, 2, 6, 19, 68, 255, 989, 3955, 16147, 67057, 282495, 1203909, 5180147, 22480686, 98268169, 432231388, 1911944862, 8499084865, 37945861008, 170096408313, 765203667592, 3453498192794, 15632819897677, 70956387986424, 322865559744975, 1472499460157086, 6729929928075598, 30818993591307189

Offset

0,2

Links

Table of n, a(n) for n=0..27.

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, j, 1 + k, -1 + n] + aux[i, -1 + j, -1 + k, -1 + n] + aux[i, j, -1 + k, -1 + n] + aux[1 + i, -1 + j, 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: A150101 A150102 A150103 * A145868 A376077 A058122

Adjacent sequences: A150101 A150102 A150103 * A150105 A150106 A150107

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved