A150121 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), (0, 1, -1), (1, 0, 0), (1, 1, 1)}.

1, 2, 6, 20, 68, 246, 890, 3282, 12264, 46038, 174702, 664952, 2543250, 9769374, 37618194, 145377752, 562898688, 2184186964, 8492135236, 33064770660, 128960010734, 503568004634, 1968705674518, 7705343996134, 30185540568274, 118367446512154, 464517420332362, 1824323889609816

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, k, -1 + n] + aux[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: A150120 A360219 A360294 * A150122 A150123 A082679

Adjacent sequences: A150118 A150119 A150120 * A150122 A150123 A150124

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved