A149374 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), (0, 0, -1), (0, 1, -1), (1, 0, 1)}.

1, 1, 4, 12, 47, 162, 711, 2793, 12113, 49196, 221666, 942290, 4229610, 18235322, 83386846, 367729931, 1678926008, 7460343556, 34432541595, 155038893329, 715065882121, 3234817528840, 15025104684796, 68555045599390, 318330259560687, 1457036761790380, 6799065794238751, 31305388241800917

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[i, -1 + j, 1 + k, -1 + n] + aux[i, j, 1 + 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: A151464 A101225 A000775 * A149375 A035310 A022016

Adjacent sequences: A149371 A149372 A149373 * A149375 A149376 A149377

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved