A148247 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, 1), (-1, 0, 0), (0, 1, 0), (1, -1, -1), (1, -1, 1)}.

1, 1, 2, 4, 13, 36, 120, 389, 1333, 4544, 16359, 59002, 215082, 798359, 3015941, 11408878, 43503397, 167952084, 652211220, 2542787190, 9987901113, 39451669571, 156290211436, 622328685876, 2490594512648, 9994139258262, 40221978823781, 162555060685885, 658864667393444, 2676378884066403

Offset

0,3

Links

Table of n, a(n) for n=0..29.

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[i, -1 + j, k, -1 + n] + aux[1 + i, j, k, -1 + n] + aux[1 + i, 1 + 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: A148244 A148245 A148246 * A148248 A148249 A148250

Adjacent sequences: A148244 A148245 A148246 * A148248 A148249 A148250

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved