A149751 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), (1, -1, 1), (1, 1, -1), (1, 1, 1)}.

1, 1, 5, 17, 81, 331, 1567, 6917, 32993, 151045, 725821, 3392889, 16395681, 77672623, 376945023, 1802187471, 8775092203, 42233825271, 206187157371, 997354857219, 4879632943263, 23695900004955, 116141608476923, 565757624024903, 2777158699418331, 13562804932211847, 66662346524949199, 326247423633847089

Offset

0,3

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, -1 + j, -1 + k, -1 + n] + aux[-1 + i, -1 + j, 1 + k, -1 + n] + aux[-1 + 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: A149749 A149750 A179605 * A303713 A188231 A023253

Adjacent sequences: A149748 A149749 A149750 * A149752 A149753 A149754

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved