A150148 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, 1, 1), (1, 0, 1), (1, 1, -1)}.

1, 2, 6, 20, 74, 268, 1030, 3906, 15198, 58918, 231154, 905668, 3573882, 14088310, 55797584, 220846346, 876736760, 3479658980, 13836948432, 55020160932, 219061193918, 872210242498, 3475925066604, 13853110396354, 55246428235236, 220342122237434, 879209773337170, 3508545125483228

Offset

0,2

Links

Table of n, a(n) for n=0..27.

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, -1 + k, -1 + n] + aux[i, -1 + 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: A150145 A150146 A150147 * A150149 A150150 A150151

Adjacent sequences: A150145 A150146 A150147 * A150149 A150150 A150151

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved