A149091 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, -1, 1), (-1, 0, 0), (0, 0, -1), (1, 1, 0)}.

1, 1, 4, 8, 31, 83, 309, 977, 3571, 12395, 45458, 165876, 617495, 2316191, 8773838, 33493548, 128840353, 498456315, 1941252054, 7594394344, 29871433149, 117966578225, 467857554197, 1862361268887, 7438937047067, 29811320860773, 119819502795074, 482960010597006, 1951744104721491

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, k, -1 + n] + aux[i, j, 1 + k, -1 + n] + aux[1 + i, j, k, -1 + n] + aux[1 + i, 1 + 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: A082595 A262154 A080072 * A149092 A188117 A094502

Adjacent sequences: A149088 A149089 A149090 * A149092 A149093 A149094

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved