A149065 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), (-1, 1, 1), (0, 1, 1), (1, -1, 0), (1, 0, -1)}.

1, 1, 3, 11, 40, 163, 675, 2886, 12689, 56478, 255603, 1168905, 5394434, 25095146, 117492138, 553152779, 2616933716, 12431990751, 59275716489, 283546088317, 1360204934717, 6541812163277, 31534431432856, 152322880776339, 737149995058359, 3573391008758199, 17349000852646641, 84349149920751191

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, j, 1 + k, -1 + n] + aux[-1 + i, 1 + j, k, -1 + n] + aux[i, -1 + j, -1 + k, -1 + n] + aux[1 + i, -1 + 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: A149063 A242467 A149064 * A131526 A329261 A073622

Adjacent sequences: A149062 A149063 A149064 * A149066 A149067 A149068

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved