A150941 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, 0, -1), (0, 1, -1), (1, 0, 1), (1, 1, 1)}.

1, 2, 9, 34, 159, 675, 3266, 14752, 71900, 334494, 1644710, 7801018, 38489940, 184758909, 914823470, 4430102086, 21974797572, 107063486966, 532012176938, 2604366673349, 12954847057435, 63641174463538, 316886312450832, 1561161633834488, 7778437729645414, 38405539491203206, 191471816504000219

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, -1 + j, 1 + k, -1 + n] + aux[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: A151307 A150939 A150940 * A150942 A150943 A150944

Adjacent sequences: A150938 A150939 A150940 * A150942 A150943 A150944

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved