A150792 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, 1, 0), (1, 0, 0), (1, 1, -1), (1, 1, 1)}

1, 2, 8, 30, 138, 594, 2839, 12892, 62672, 292932, 1436996, 6835949, 33718615, 162274753, 803263075, 3897110532, 19337079017, 94365819222, 469026208827, 2298901953651, 11440293086123, 56262404021750, 280242464558274, 1381838922334531, 6887750756939698, 34033897373797286, 169733701806981701

Offset

0,2

Links

Table of n, a(n) for n=0..26.

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, -1 + j, 1 + k, -1 + n] + aux[-1 + i, j, k, -1 + n] + aux[1 + i, -1 + j, 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: A150790 A150791 A026693 * A302187 A266043 A358962

Adjacent sequences: A150789 A150790 A150791 * A150793 A150794 A150795

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved