A149245 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), (-1, 0, 1), (0, -1, 1), (1, 1, 0)}.

1, 1, 4, 11, 36, 138, 470, 1811, 6957, 26509, 106308, 418838, 1680174, 6831180, 27657994, 113594502, 467388473, 1929858509, 8021111685, 33391836563, 139565619390, 585228693864, 2459366708678, 10363035574570, 43773488086081, 185231446531915, 785496551225606, 3337214105223772

Offset

0,3

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, k, -1 + n] + aux[i, 1 + j, -1 + k, -1 + n] + aux[1 + i, j, -1 + 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: A112849 A372721 A149244 * A054105 A300772 A238244

Adjacent sequences: A149242 A149243 A149244 * A149246 A149247 A149248

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved