A150923 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), (0, 0, 1), (0, 1, -1), (1, 0, -1), (1, 1, 1)}.

1, 2, 9, 33, 145, 624, 2811, 12770, 59045, 274746, 1291347, 6099917, 28987799, 138336728, 662762769, 3185314137, 15353072483, 74180403680, 359207508273, 1742771595073, 8470077478449, 41229298992010, 200969968948619, 980856465445634, 4792716506836087, 23443124281677520, 114780479390363687

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, 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: A202206 A150921 A150922 * A150924 A150925 A150926

Adjacent sequences: A150920 A150921 A150922 * A150924 A150925 A150926

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved