A149946 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, 1), (0, 0, -1), (0, 1, 0), (1, 0, 1)}

1, 2, 5, 15, 50, 169, 582, 2060, 7422, 27036, 99396, 368485, 1375316, 5162128, 19472276, 73760245, 280411398, 1069469986, 4090621127, 15686273759, 60288482091, 232187218317, 895879809936, 3462537777602, 13403241563300, 51956190839194, 201663622683249, 783677199027033, 3048787038817415

Offset

0,2

Links

Table of n, a(n) for n=0..28.

Alin Bostan and Manuel Kauers, Automatic Classification of Restricted Lattice Walks, arXiv:0811.2899 [math.CO], 2008-2009.

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, k, -1 + n] + aux[i, j, 1 + k, -1 + n] + aux[1 + i, 1 + j, -1 + 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: A202182 A149944 A149945 * A149947 A149948 A093129

Adjacent sequences: A149943 A149944 A149945 * A149947 A149948 A149949

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved