A149463 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, 1, -1), (1, 1, 1)}.

1, 1, 4, 13, 52, 190, 760, 2911, 11644, 45526, 182104, 719158, 2876632, 11420476, 45681904, 181897393, 727589572, 2902122838, 11608491352, 46350498442, 185401993768, 740747412928, 2962989651712, 11842961166202, 47371844664808, 189392208541144, 757568834164576, 3029258755839088

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[-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: A223899 A357962 A097169 * A323791 A149464 A307398

Adjacent sequences: A149460 A149461 A149462 * A149464 A149465 A149466

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved