A150842 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, 0, 0), (0, 1, 1), (1, -1, 0), (1, 1, -1), (1, 1, 0)}.

1, 2, 8, 32, 138, 612, 2782, 12835, 59916, 282151, 1337920, 6379086, 30552956, 146880837, 708342744, 3425171883, 16600524520, 80617576576, 392192150420, 1910910968991, 9323518359408, 45546419600056, 222746154981758, 1090440406459158, 5343057270195160, 26202306700463284, 128594087415902160

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, k, -1 + n] + aux[-1 + i, -1 + j, 1 + k, -1 + n] + aux[-1 + i, 1 + j, k, -1 + n] + aux[i, -1 + j, -1 + k, -1 + n] + aux[1 + i, 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: A150839 A150840 A150841 * A274483 A308152 A150843

Adjacent sequences: A150839 A150840 A150841 * A150843 A150844 A150845

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved