A149341 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), (-1, 1, 1), (0, 1, -1), (1, 0, 1)}.

1, 1, 4, 12, 41, 150, 568, 2173, 8481, 33756, 135463, 547375, 2233624, 9174167, 37848374, 156914675, 653597162, 2731737145, 11452844102, 48166309663, 203115207619, 858494466299, 3636552361349, 15436162344558, 65641966321937, 279610928461517, 1192948785566952, 5097192013993835

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, j, -1 + k, -1 + n] + aux[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, 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: A308369 A275184 A354338 * A149342 A149343 A225586

Adjacent sequences: A149338 A149339 A149340 * A149342 A149343 A149344

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved