A149586 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, 0, -1), (1, -1, -1), (1, 1, 1)}

1, 1, 5, 15, 55, 215, 875, 3533, 14769, 63025, 271061, 1171573, 5125689, 22634577, 100374805, 446869675, 2001901659, 9014772611, 40708594111, 184335519819, 837884736507, 3821043268147, 17460417237311, 79944561997591, 366975174492475, 1688354607241075, 7779433515441811, 35898846545834367

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, -1 + k, -1 + n] + aux[-1 + i, 1 + j, 1 + k, -1 + n] + aux[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: A149585 A114947 A316104 * A149587 A149588 A137959

Adjacent sequences: A149583 A149584 A149585 * A149587 A149588 A149589

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved