A148874 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, 1), (0, 1, -1), (0, 1, 1), (1, -1, 0)}.

1, 1, 3, 8, 29, 97, 356, 1345, 5312, 20951, 84910, 349614, 1456834, 6106706, 25935852, 111040569, 477930029, 2069560858, 9025183157, 39530097395, 173797714040, 767680927436, 3404799777699, 15144014386727, 67566885275210, 302450951239750, 1357363670407487, 6105291074781927, 27528978458057805

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, k, -1 + n] + aux[i, -1 + j, -1 + k, -1 + n] + aux[i, -1 + j, 1 + k, -1 + n] + aux[1 + i, j, -1 + 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: A148871 A148872 A148873 * A022017 A148875 A338306

Adjacent sequences: A148871 A148872 A148873 * A148875 A148876 A148877

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved