A149352 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, 1, 0), (0, 0, -1), (1, 0, 1), (1, 1, -1)}.

1, 1, 4, 12, 42, 157, 637, 2501, 10164, 42658, 180400, 764722, 3307143, 14430374, 62996763, 276911209, 1228976451, 5469146618, 24404767964, 109552267142, 493669549335, 2227647563738, 10084056179245, 45818706625373, 208578109286625, 951168969946909, 4349255976194362, 19927255165939965

Offset

0,3

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, 1 + k, -1 + n] + aux[-1 + i, j, -1 + k, -1 + n] + aux[i, j, 1 + k, -1 + n] + aux[1 + i, -1 + 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: A149349 A149350 A149351 * A149353 A149354 A197659

Adjacent sequences: A149349 A149350 A149351 * A149353 A149354 A149355

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved