A148322 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), (-1, 1, 1), (0, -1, 0), (0, 0, 1), (1, 0, -1)}.

1, 1, 2, 5, 14, 41, 132, 442, 1524, 5470, 20059, 74978, 286336, 1108833, 4349771, 17293196, 69428179, 281307331, 1150317126, 4738033915, 19649014226, 82036268908, 344417930644, 1453617282097, 6166684567631, 26276294251448, 112432261367960, 483045501643010, 2082734215839570

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, j, 1 + k, -1 + n] + aux[i, j, -1 + k, -1 + n] + aux[i, 1 + j, k, -1 + n] + aux[1 + 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: A222589 A243870 A287968 * A148323 A148324 A000660

Adjacent sequences: A148319 A148320 A148321 * A148323 A148324 A148325

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved