A148720 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, 0, 0), (0, -1, 1), (0, 1, 0), (1, -1, 0), (1, 1, -1)}.

1, 1, 3, 7, 24, 76, 277, 1012, 3900, 15298, 61744, 252844, 1055394, 4456946, 19066780, 82383168, 359267491, 1579448039, 6994656090, 31175776248, 139782570970, 630064954347, 2853843406073, 12983914841969, 59312608158319, 271967699137691, 1251392188397235, 5776438662674473, 26743675660270307

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, -1 + j, 1 + k, -1 + n] + aux[-1 + i, 1 + j, k, -1 + n] + aux[i, -1 + j, k, -1 + n] + aux[i, 1 + j, -1 + k, -1 + n] + aux[1 + i, 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: A148719 A138541 A290750 * A225826 A228992 A246657

Adjacent sequences: A148717 A148718 A148719 * A148721 A148722 A148723

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved