A149315 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, 0), (1, -1, 1), (1, 1, -1), (1, 1, 0)}.

1, 1, 4, 11, 50, 179, 844, 3400, 16351, 70268, 341854, 1528459, 7490503, 34379761, 169311818, 791428328, 3910978136, 18525118321, 91772597075, 439023657803, 2178920977547, 10502920105982, 52200231902042, 253113688816381, 1259356840268939, 6135341868509264, 30552135452224128, 149410855632996375

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[-1 + i, -1 + j, 1 + k, -1 + n] + aux[-1 + i, 1 + j, -1 + k, -1 + n] + aux[1 + i, -1 + j, 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: A149312 A149313 A149314 * A149316 A271426 A318120

Adjacent sequences: A149312 A149313 A149314 * A149316 A149317 A149318

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved