A150103 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, 0, 1), (0, 1, 1), (1, 0, -1)}.

1, 2, 6, 19, 68, 255, 984, 3929, 16013, 66253, 278482, 1183947, 5079517, 21992997, 95913334, 420824859, 1857477019, 8239560040, 36707294405, 164224110552, 737390796048, 3321642113284, 15009789841105, 68013861083631, 308958608029480, 1406890127444539, 6420448495277942, 29358341405419166

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, j, 1 + k, -1 + n] + aux[i, -1 + j, -1 + k, -1 + n] + aux[i, 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: A150100 A150101 A150102 * A150104 A145868 A376077

Adjacent sequences: A150100 A150101 A150102 * A150104 A150105 A150106

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved