A149729 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, 1, -1), (1, 0, -1), (1, 1, 1)}.

1, 1, 5, 17, 75, 289, 1329, 5635, 26397, 116593, 552593, 2506239, 11979623, 55316481, 266066767, 1244457787, 6014193317, 28401812231, 137771141551, 655491800229, 3189195262765, 15263886550913, 74447327834795, 358032324714527, 1749853945686871, 8448874986136843, 41365559604166123, 200391378903857941

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, j, 1 + k, -1 + n] + aux[i, -1 + 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: A149726 A149727 A149728 * A282963 A149730 A149731

Adjacent sequences: A149726 A149727 A149728 * A149730 A149731 A149732

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved