A148939 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), (1, -1, 0), (1, 1, -1)}.

1, 1, 3, 9, 29, 97, 337, 1200, 4352, 15964, 59163, 221154, 832740, 3153898, 12001752, 45860585, 175873274, 676595506, 2610061582, 10092824792, 39110984254, 151848868126, 590564253255, 2300328671191, 8972524560949, 35041779245101, 137011117055180, 536266828836428, 2100987903534724

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, -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: A081696 A247172 A339843 * A346158 A077587 A001893

Adjacent sequences: A148936 A148937 A148938 * A148940 A148941 A148942

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved