A148117 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, -1, 1), (-1, 0, 0), (0, 1, 0), (1, -1, 0)}.

1, 1, 2, 4, 11, 26, 70, 195, 586, 1662, 5068, 15965, 50052, 157178, 513731, 1686164, 5537693, 18364576, 62042980, 210460928, 712129270, 2441118300, 8465730672, 29229162000, 101493128823, 356292793377, 1251427851901, 4403651455081, 15587741497401, 55409301916782, 197456798358821, 704509180319693

Offset

0,3

Links

Table of n, a(n) for n=0..31.

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, k, -1 + n] + aux[1 + i, j, k, -1 + n] + aux[1 + i, 1 + j, -1 + 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: A159336 A240571 A151257 * A148118 A148119 A148120

Adjacent sequences: A148114 A148115 A148116 * A148118 A148119 A148120

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved