A150813 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), (-1, 0, 1), (0, 0, 1), (1, 0, -1), (1, 1, 1)}

1, 2, 8, 31, 135, 585, 2649, 12019, 55654, 258542, 1214385, 5721966, 27142088, 129101750, 616801930, 2953712052, 14188995038, 68294147421, 329480324924, 1592172521561, 7707938731918, 37367301758612, 181416571489690, 881817419169136, 4291413855482241, 20905775215087554, 101945736560909613

Offset

0,2

Links

Table of n, a(n) for n=0..26.

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, j, -1 + k, -1 + n] + aux[1 + 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: A150810 A150811 A150812 * A150814 A150815 A150816

Adjacent sequences: A150810 A150811 A150812 * A150814 A150815 A150816

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved