A148403 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, 0, 0), (0, -1, 1), (0, 0, 1), (1, 1, -1)}.

1, 1, 2, 5, 17, 50, 166, 592, 2132, 7747, 29345, 113657, 439653, 1731991, 6959797, 28044519, 113767591, 467788415, 1936625448, 8035496503, 33615931265, 141684937750, 598464920684, 2538728461839, 10838186244657, 46414416433134, 199214751992087, 858994498480348, 3717461948696793

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[i, j, -1 + k, -1 + n] + aux[i, 1 + j, -1 + k, -1 + n] + aux[1 + i, j, 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: A368756 A148401 A148402 * A148404 A061675 A148405

Adjacent sequences: A148400 A148401 A148402 * A148404 A148405 A148406

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved