A149298 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, 1, 1), (0, 0, -1), (1, 0, -1), (1, 0, 1)}.

1, 1, 4, 11, 46, 163, 711, 2795, 12428, 51753, 235649, 1018677, 4692842, 20793843, 96868626, 437325625, 2053558366, 9396741255, 44410201233, 205466708855, 976289490566, 4555528967641, 21739565731106, 102161620436227, 489367738092226, 2313227779931447, 11115478974146769, 52801134542954409

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[-1 + i, j, 1 + k, -1 + n] + aux[i, j, 1 + k, -1 + n] + aux[1 + i, -1 + 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: A149295 A149296 A149297 * A149299 A149300 A149301

Adjacent sequences: A149295 A149296 A149297 * A149299 A149300 A149301

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved