A150793 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, 0, 0), (0, -1, 0), (0, 1, -1), (1, 0, 1), (1, 1, 0)}

1, 2, 8, 31, 129, 561, 2490, 11245, 51533, 238676, 1114413, 5240536, 24788101, 117813202, 562262025, 2693085867, 12939283871, 62336917334, 301041033610, 1456918032898, 7064316729091, 34312084903893, 166914996786011, 813112960416231, 3966047836697198, 19367308710719144, 94676630096016922

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, k, -1 + n] + aux[-1 + i, j, -1 + k, -1 + n] + aux[i, -1 + j, 1 + k, -1 + n] + aux[i, 1 + j, k, -1 + n] + aux[1 + i, 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: A281831 A206229 A027073 * A150794 A150795 A027078

Adjacent sequences: A150790 A150791 A150792 * A150794 A150795 A150796

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved