A151244 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), (0, 0, 1), (0, 1, 0), (1, 0, 1), (1, 1, 0)}

1, 4, 16, 70, 322, 1498, 7094, 34036, 164048, 796202, 3885290, 19002928, 93264752, 459007438, 2262036586, 11169376970, 55240445346, 273433650434, 1355096702100, 6722446090996, 33368104779532, 165759411164920, 823978800776782, 4097584417473362, 20387964048849642, 101489536218814760

Offset

0,2

Links

Table of n, a(n) for n=0..25.

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[-1 + i, j, -1 + k, -1 + n] + aux[i, -1 + j, k, -1 + n] + aux[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: A144316 A180145 A133789 * A280767 A091354 A326654

Adjacent sequences: A151241 A151242 A151243 * A151245 A151246 A151247

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved