A148395 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), (1, 0, -1), (1, 0, 0)}.

1, 1, 2, 5, 16, 53, 194, 678, 2540, 9864, 39339, 159002, 650824, 2696290, 11362478, 48339341, 207535853, 897905427, 3913431910, 17176437470, 75847364805, 336777968274, 1503202127905, 6739922000073, 30346283721419, 137170213293591, 622379744415404, 2833871341615016, 12943682517721161

Offset

0,3

Links

Table of n, a(n) for n=0..28.

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, k, -1 + n] + aux[-1 + i, 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: A047006 A127498 A149958 * A148396 A108521 A148397

Adjacent sequences: A148392 A148393 A148394 * A148396 A148397 A148398

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved