A148397 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), (-1, 1, 1), (0, 0, -1), (1, 0, 0), (1, 1, -1)}.

1, 1, 2, 5, 16, 53, 201, 735, 2865, 11311, 45866, 189465, 796172, 3381641, 14561199, 63187193, 276872754, 1222044791, 5430760602, 24286138255, 109201747174, 493481357555, 2240419937667, 10213170677321, 46739370653550, 214646461546109, 988964308208578, 4570386968516601, 21180640601186075

Offset

0,3

Links

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

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, j, k, -1 + n] + aux[i, j, 1 + k, -1 + n] + aux[1 + i, -1 + 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: A148395 A148396 A108521 * A148398 A346518 A100442

Adjacent sequences: A148394 A148395 A148396 * A148398 A148399 A148400

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved