A150220 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, 1), (0, 0, 1), (0, 1, 0), (1, -1, 0), (1, 1, -1)}.

1, 2, 6, 21, 82, 339, 1461, 6482, 29384, 135426, 632225, 2981872, 14180688, 67895415, 326899704, 1581320373, 7679588620, 37420701756, 182865431382, 895826999202, 4397905180052, 21630991920019, 106564981184354, 525743716070770, 2597058893692578, 12843243481920950, 63576790918965557, 314997058625176355

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, 1 + k, -1 + n] + aux[-1 + i, 1 + j, k, -1 + n] + aux[i, -1 + j, k, -1 + n] + aux[i, j, -1 + k, -1 + n] + aux[1 + i, 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: A150217 A150218 A150219 * A168653 A279567 A281784

Adjacent sequences: A150217 A150218 A150219 * A150221 A150222 A150223

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved