A149885 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, -1), (0, 0, 1), (1, -1, 0), (1, 0, 1)}.

1, 2, 5, 14, 44, 151, 535, 1966, 7405, 28505, 111788, 445140, 1795088, 7320770, 30148959, 125206603, 523997043, 2207912732, 9359648685, 39898730194, 170940133097, 735708995287, 3179865260996, 13797390440690, 60080114591020, 262490678495536, 1150372266528940, 5055989555564113

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[-1 + i, 1 + j, k, -1 + n] + aux[i, j, -1 + k, -1 + n] + aux[1 + i, -1 + j, 1 + 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: A360592 A363431 A149884 * A149886 A207081 A148336

Adjacent sequences: A149882 A149883 A149884 * A149886 A149887 A149888

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved