A150768 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, 0), (0, 0, -1), (1, 0, 0), (1, 1, 1)}

1, 2, 8, 30, 128, 546, 2414, 10856, 49400, 226878, 1053341, 4911942, 23065184, 108766594, 515154967, 2448386241, 11672043990, 55807469114, 267451716801, 1284557001388, 6182325559111, 29805956507042, 143934962407235, 696107584579056, 3371174760656563, 16346570988382705, 79354842703323609

Offset

0,2

Links

Table of n, a(n) for n=0..26.

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[-1 + i, j, k, -1 + n] + aux[i, j, 1 + k, -1 + n] + aux[1 + i, -1 + j, 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: A150765 A150766 A150767 * A150769 A150770 A150771

Adjacent sequences: A150765 A150766 A150767 * A150769 A150770 A150771

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved