A149957 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, 0, 1), (0, 1, -1), (0, 1, 0), (1, 0, 0)}

1, 2, 5, 16, 52, 182, 669, 2504, 9698, 38195, 152767, 621076, 2549560, 10581714, 44310835, 186883460, 794030970, 3393309246, 14581119513, 62974335852, 273154359474, 1189789622673, 5201720413303, 22819093413662, 100426881360373, 443259890866905, 1961797012311293, 8704741535659198

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, k, -1 + n] + aux[i, -1 + j, k, -1 + n] + aux[i, -1 + j, 1 + k, -1 + n] + aux[1 + i, 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: A337268 A148392 A149956 * A148393 A148394 A291685

Adjacent sequences: A149954 A149955 A149956 * A149958 A149959 A149960

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved