A149569 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, 0), (-1, 1, -1), (1, -1, 0), (1, -1, 1), (1, 1, 1)}

1, 1, 5, 13, 63, 201, 991, 3543, 17521, 66375, 329361, 1299919, 6461629, 26223915, 130525411, 541026087, 2695329199, 11354835089, 56607090975, 241583878837, 1204988720797, 5197181851895, 25933310360265, 112838742024709, 563231409876969, 2468935733666465, 12326783508725881, 54379000362010723

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, k, -1 + n] + aux[1 + i, -1 + j, 1 + k, -1 + n] + aux[1 + i, 1 + j, 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: A144725 A051902 A269514 * A149570 A149571 A149572

Adjacent sequences: A149566 A149567 A149568 * A149570 A149571 A149572

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved