A150355 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), (-1, 0, -1), (0, -1, -1), (0, 0, 1), (1, 1, 1)}.

1, 2, 7, 23, 91, 350, 1437, 5838, 24607, 103920, 446477, 1922851, 8368785, 36609466, 161205477, 712423109, 3162363453, 14091280408, 63018998437, 282639322289, 1270975244989, 5730127684774, 25897263015151, 117291371020034, 532224610374637, 2419429040503232, 11017876743090397, 50255543946664639

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[i, j, -1 + k, -1 + n] + aux[i, 1 + j, 1 + k, -1 + n] + aux[1 + i, 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: A150352 A150353 A150354 * A150356 A150357 A150358

Adjacent sequences: A150352 A150353 A150354 * A150356 A150357 A150358

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved