A149927 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, -1), (0, -1, 1), (0, 1, 0), (1, 0, 0)}.

1, 2, 5, 15, 48, 163, 573, 2093, 7827, 29830, 115754, 455939, 1817086, 7316796, 29756708, 122012669, 503813023, 2094285936, 8759168442, 36826653285, 155577457016, 660287621380, 2813953261588, 12036662291890, 51668602454264, 222532058296393, 961307279118620, 4164329282317083

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, j, k, -1 + n] + aux[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, 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: A203067 A278077 A145072 * A035350 A006570 A149928

Adjacent sequences: A149924 A149925 A149926 * A149928 A149929 A149930

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved