A148123 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, 0), (1, 0, 1)}.

1, 1, 2, 4, 11, 26, 75, 200, 615, 1734, 5590, 16378, 54142, 164546, 551565, 1719056, 5850985, 18558052, 63934146, 205992946, 715984848, 2338641028, 8186888340, 27034793372, 95278888170, 317483080156, 1125094282972, 3779967420752, 13457694265926, 45541140013964, 162805944879609, 554376697149596

Offset

0,3

Links

Table of n, a(n) for n=0..31.

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, -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, -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: A148120 A148121 A148122 * A148124 A148125 A148126

Adjacent sequences: A148120 A148121 A148122 * A148124 A148125 A148126

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved