A149181 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, 0), (0, -1, 1), (0, 0, -1), (1, 1, 0)}.

1, 1, 4, 10, 36, 120, 448, 1630, 6386, 24438, 98525, 390708, 1608407, 6538477, 27359803, 113310781, 480282169, 2018226689, 8644468533, 36752277408, 158790149990, 681619870031, 2966636460984, 12837509053025, 56224797917440, 244975206360553, 1078774565372709, 4728171786376264, 20920372928367658

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[i, j, 1 + k, -1 + n] + aux[i, 1 + j, -1 + k, -1 + n] + aux[1 + i, j, 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: A088013 A149179 A149180 * A149182 A149183 A369554

Adjacent sequences: A149178 A149179 A149180 * A149182 A149183 A149184

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved