A149421 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, 0, 1), (1, 1, -1)}.

1, 1, 4, 12, 56, 194, 936, 3538, 17321, 68903, 339902, 1396514, 6919349, 29062278, 144387889, 616244809, 3067086814, 13251144642, 66031397048, 288051494440, 1436595469141, 6316268935590, 31520173742537, 139490497666088, 696411055283854, 3098956054640149, 15476764066529596, 69196679300334168

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, 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: A092576 A149420 A298680 * A051195 A179607 A149422

Adjacent sequences: A149418 A149419 A149420 * A149422 A149423 A149424

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved