A148227 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, 0, 1), (1, 0, 0), (1, 1, -1)}.

1, 1, 2, 4, 13, 32, 107, 303, 1129, 3434, 13071, 42148, 167993, 561875, 2267904, 7834604, 32442310, 114598028, 478406714, 1725209229, 7320631607, 26799600927, 114360856625, 424737947485, 1833141175429, 6882799867886, 29828067212451, 113195225162010, 494672858704167, 1892803590856411

Offset

0,3

Links

Table of n, a(n) for n=0..29.

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, k, -1 + 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]]; Table[Sum[aux[i, j, k, n], {i, 0, n}, {j, 0, n}, {k, 0, n}], {n, 0, 10}]

Crossrefs

Sequence in context: A004644 A000866 A320424 * A148228 A148229 A148230

Adjacent sequences: A148224 A148225 A148226 * A148228 A148229 A148230

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved