A148112 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, 0, 1), (0, 1, -1), (1, -1, 0), (1, 0, 0)}.

1, 1, 2, 4, 10, 29, 84, 269, 881, 2978, 10534, 37631, 138156, 517621, 1961323, 7567042, 29532445, 116500782, 464882279, 1870733737, 7594358700, 31071320808, 127996498806, 530873129314, 2214683900392, 9291484415679, 39188034692063, 166050612886805, 706884457310860, 3021936095511674

Offset

0,3

Links

Table of n, a(n) for n=0..29.

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, k, -1 + n] + aux[-1 + i, 1 + j, k, -1 + n] + aux[i, -1 + j, 1 + k, -1 + n] + aux[1 + i, 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: A189582 A060315 A148111 * A224845 A148113 A243814

Adjacent sequences: A148109 A148110 A148111 * A148113 A148114 A148115

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved