A148072 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, 0), (0, 0, 1), (1, 0, -1)}.

1, 1, 2, 4, 9, 21, 56, 148, 421, 1207, 3535, 10407, 31879, 97111, 304344, 958636, 3045621, 9696563, 31478459, 101764723, 334038583, 1100234409, 3639933291, 12057585459, 40418753669, 135042191401, 455549125751, 1540601216083, 5223311667307, 17725604119599, 60646085848546, 206928271796266, 710805289086933

Offset

0,3

Links

Table of n, a(n) for n=0..32.

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, j, -1 + k, -1 + n] + aux[1 + i, -1 + 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: A032129 A304914 A005217 * A001430 A148073 A057513

Adjacent sequences: A148069 A148070 A148071 * A148073 A148074 A148075

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved