A148753 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, 0), (1, -1, 0), (1, 0, 1)}.

1, 1, 3, 7, 28, 77, 326, 1028, 4508, 15255, 68632, 243837, 1114866, 4107946, 19004015, 71988788, 336043828, 1301048142, 6116392715, 24103744170, 113963361244, 455754834422, 2164963692051, 8765929019818, 41804416460392, 171069967405773, 818553601362454, 3380530240851678, 16222030587174635

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[1 + i, -1 + j, 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: A101303 A148751 A148752 * A148754 A148755 A148756

Adjacent sequences: A148750 A148751 A148752 * A148754 A148755 A148756

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved