A149186 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, 0), (-1, 0, 1), (-1, 1, -1), (0, -1, 1), (1, 1, 0)}.

1, 1, 4, 10, 36, 125, 454, 1722, 6609, 25843, 102590, 411104, 1663187, 6782912, 27831566, 114882503, 476493101, 1985031001, 8300902795, 34833257984, 146612269660, 618823561050, 2618412456313, 11104706758264, 47192773402321, 200945045039469, 857117045058559, 3661934564079485

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, -1 + j, 1 + k, -1 + n] + aux[1 + i, j, -1 + k, -1 + n] + aux[1 + i, 1 + j, 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: A369554 A149184 A149185 * A345245 A197552 A378732

Adjacent sequences: A149183 A149184 A149185 * A149187 A149188 A149189

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved