A150151 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, 1, -1), (0, 1, 1), (1, -1, -1), (1, 1, 0)}.

1, 2, 6, 20, 74, 274, 1103, 4366, 18185, 75130, 320230, 1358179, 5888175, 25443837, 111664081, 489304865, 2168190791, 9601100796, 42882613069, 191466467335, 860762279600, 3869278985555, 17489846419136, 79063930975662, 359042915610462, 1630838121006658, 7435489235481713, 33912055201761025

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, k, -1 + n] + aux[-1 + i, 1 + j, 1 + k, -1 + n] + aux[i, -1 + j, -1 + k, -1 + n] + aux[1 + 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: A150148 A150149 A150150 * A374599 A361753 A376811

Adjacent sequences: A150148 A150149 A150150 * A150152 A150153 A150154

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved