A149182 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), (1, -1, 0), (1, 1, 0)}.

1, 1, 4, 10, 36, 120, 451, 1626, 6426, 24185, 98084, 381500, 1568582, 6253145, 25945355, 105297818, 440103945, 1809396632, 7609736345, 31591826888, 133555292794, 558736339296, 2372175262534, 9986627300516, 42550513983270, 180067731713734, 769559478434464, 3270867038266924, 14015828521820036

Offset

0,3

Links

Table of n, a(n) for n=0..28.

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, k, -1 + n] + aux[-1 + i, 1 + j, 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: A149179 A149180 A149181 * A149183 A369554 A149184

Adjacent sequences: A149179 A149180 A149181 * A149183 A149184 A149185

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved