A150858 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), (1, -1, 0), (1, 0, 0), (1, 1, -1), (1, 1, 1)}.

1, 2, 8, 32, 142, 630, 2890, 13302, 62276, 292766, 1389404, 6615274, 31675542, 152069340, 732818002, 3539103044, 17137709066, 83134827968, 404087736826, 1966989170818, 9589474380948, 46807426842820, 228752844566004, 1119079362907250, 5480116816480130, 26859252084266098, 131752905332701178

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, -1 + j, 1 + k, -1 + n] + aux[-1 + i, j, k, -1 + n] + aux[-1 + 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: A150856 A105483 A150857 * A150859 A150860 A308368

Adjacent sequences: A150855 A150856 A150857 * A150859 A150860 A150861

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved