A148242 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, -1), (-1, 1, 1), (0, 0, -1), (1, 0, 0)}.

1, 1, 2, 4, 13, 36, 115, 342, 1139, 3764, 12958, 44395, 155181, 549379, 1971824, 7110201, 25895872, 94857236, 350624428, 1302239497, 4858414337, 18230049290, 68700089837, 260092887599, 988164427994, 3765690820956, 14407647305594, 55282778658419, 212749959207908, 820917116037383, 3174828575276883

Offset

0,3

Links

Table of n, a(n) for n=0..30.

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, j, 1 + k, -1 + n] + aux[1 + i, -1 + j, -1 + k, -1 + n] + aux[1 + i, -1 + 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: A148240 A151354 A148241 * A148243 A148244 A148245

Adjacent sequences: A148239 A148240 A148241 * A148243 A148244 A148245

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved