A148932 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, 0), (-1, 0, 0), (0, -1, 1), (0, 1, 1), (1, 0, -1)}.

1, 1, 3, 9, 28, 97, 349, 1302, 4948, 19260, 76305, 306502, 1244827, 5110421, 21175303, 88391007, 371584013, 1571765178, 6684742369, 28573868325, 122690873139, 528944280447, 2289098069619, 9940723089700, 43304254195744, 189206292581281, 828943812897922, 3640845471311392, 16029356622087075

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, j, 1 + k, -1 + n] + aux[i, -1 + j, -1 + k, -1 + n] + aux[i, 1 + j, -1 + k, -1 + n] + aux[1 + i, j, k, -1 + n] + aux[1 + i, 1 + 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: A366859 A148931 A243599 * A151421 A148933 A148934

Adjacent sequences: A148929 A148930 A148931 * A148933 A148934 A148935

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved