A148016 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, 1, 0), (0, 1, -1), (1, 0, 0)}.

1, 1, 2, 3, 8, 17, 46, 117, 337, 954, 2765, 8334, 25350, 78302, 244664, 777806, 2495210, 8049224, 26288829, 86510067, 286120463, 952818316, 3193840880, 10759053541, 36391963273, 123723824745, 422498010677, 1447387300427, 4976890447866, 17175794352740, 59448688148611, 206336010280396, 718237279107642

Offset

0,3

Links

Table of n, a(n) for n=0..32.

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, k, -1 + n] + aux[i, -1 + j, 1 + k, -1 + n] + aux[1 + i, -1 + 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: A292852 A148014 A148015 * A148017 A148018 A148019

Adjacent sequences: A148013 A148014 A148015 * A148017 A148018 A148019

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved