A148083 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, 0, 1), (0, 1, -1), (1, -1, 0)}.

1, 1, 2, 4, 9, 24, 68, 204, 635, 2048, 6684, 22581, 77989, 271706, 968228, 3500939, 12729468, 47024807, 175664979, 658360378, 2498042454, 9560670342, 36669158456, 142032179940, 553961114253, 2163565785558, 8518522634671, 33731910890175, 133687274886976, 533438652268653, 2138794101079053

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, 1 + j, k, -1 + n] + aux[i, -1 + j, 1 + k, -1 + n] + aux[i, 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: A148080 A148081 A148082 * A200966 A148084 A156804

Adjacent sequences: A148080 A148081 A148082 * A148084 A148085 A148086

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved