A150892 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), (0, 0, 1), (1, 1, -1), (1, 1, 1)}.

1, 2, 8, 34, 153, 704, 3315, 15792, 75956, 367912, 1791757, 8761636, 42987377, 211475259, 1042612240, 5149530008, 25472289092, 126159248997, 625514850291, 3104248839730, 15417720543162, 76627056718629, 381069298652147, 1896064966438921, 9438486217346072, 47003251263464404, 234158435724772449

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[i, j, -1 + 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: A150891 A074606 A002928 * A150893 A235038 A150894

Adjacent sequences: A150889 A150890 A150891 * A150893 A150894 A150895

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved