A149293 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, 0), (1, 0, -1), (1, 0, 1)}.

1, 1, 4, 11, 46, 147, 647, 2313, 10514, 39751, 184331, 723889, 3402792, 13737157, 65202392, 268711423, 1284588076, 5379748961, 25859980743, 109703697497, 529631702686, 2270663977323, 11000924793908, 47581223317215, 231188095777190, 1007433932569751, 4906752853395865, 21519506496620585

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[1 + i, -1 + j, 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: A363663 A149291 A149292 * A149294 A149295 A149296

Adjacent sequences: A149290 A149291 A149292 * A149294 A149295 A149296

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved