A150439 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, -1), (1, 0, 1), (1, 1, 0)}.

1, 2, 7, 24, 101, 392, 1703, 7119, 31486, 135870, 610317, 2689175, 12179773, 54466446, 248384257, 1121795909, 5143391889, 23410157731, 107778940707, 493502891246, 2280127647681, 10490012968322, 48610428832274, 224519830847282, 1043056422167442, 4833374956628301, 22504407440499129, 104571539083591522

Offset

0,2

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, -1 + j, k, -1 + n] + aux[-1 + i, j, -1 + 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, -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: A150437 A150438 A326336 * A150440 A150441 A150442

Adjacent sequences: A150436 A150437 A150438 * A150440 A150441 A150442

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved