A150129 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, 1), (1, 1, -1)}.

1, 2, 6, 20, 72, 262, 986, 3732, 14308, 55280, 214610, 837858, 3281386, 12889822, 50761728, 200279230, 791619506, 3133268528, 12416918448, 49259337824, 195589455772, 777223955192, 3090583797818, 12296847146286, 48952531584772, 194965289636094, 776814154823044, 3096239527352566

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, 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: A150128 A148480 A194950 * A360267 A360291 A150130

Adjacent sequences: A150126 A150127 A150128 * A150130 A150131 A150132

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved