A150166 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, -1, 0), (1, 1, 0)}.

1, 2, 6, 20, 75, 294, 1201, 5078, 21848, 95576, 424532, 1906655, 8636683, 39450664, 181496328, 839654187, 3904476015, 18243215608, 85580996797, 402880951625, 1902911971526, 9014705935470, 42816705935196, 203856822736059, 972780079340487, 4651358785357559, 22281663912308269, 106922886723397286

Offset

0,2

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, 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: A150165 A148482 A148483 * A150167 A150168 A145870

Adjacent sequences: A150163 A150164 A150165 * A150167 A150168 A150169

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved