A148937 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), (0, 1, 1), (1, -1, 0), (1, 0, -1)}.

1, 1, 3, 9, 28, 102, 378, 1408, 5508, 22306, 89503, 365635, 1539892, 6456566, 27184822, 116960718, 503981206, 2171078298, 9476079313, 41546823539, 182158914880, 804098318961, 3566738165143, 15847037113039, 70629009783914, 315975013994710, 1417702911326918, 6371060606606075, 28700191152776997

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[-1 + i, 1 + j, k, -1 + n] + aux[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: A148935 A148936 A121656 * A047137 A058145 A218915

Adjacent sequences: A148934 A148935 A148936 * A148938 A148939 A148940

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved