A148856 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), (0, 1, -1), (1, 0, 1)}.

1, 1, 3, 8, 28, 93, 345, 1247, 4905, 18621, 75573, 297895, 1235431, 5004478, 21069953, 87081849, 370961528, 1556555814, 6694323743, 28429384992, 123233469423, 528551018694, 2306190887973, 9973209794754, 43756896008712, 190541968507586, 839978958124485, 3679275247472375, 16287097093699275

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, -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: A148853 A148854 A148855 * A151482 A241585 A273162

Adjacent sequences: A148853 A148854 A148855 * A148857 A148858 A148859

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved