A148833 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, 1), (-1, 0, 1), (0, 1, -1), (1, -1, -1), (1, 1, 0)}.

1, 1, 3, 8, 27, 88, 330, 1233, 4757, 19087, 77084, 318057, 1332943, 5633800, 24135510, 104270601, 453822577, 1992313735, 8796237670, 39076873799, 174584332753, 783445597358, 3532945065726, 15995372227192, 72689772282113, 331560783129859, 1517023330197527, 6962862373775283, 32048845700046927

Offset

0,3

Links

Table of n, a(n) for n=0..28.

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[i, -1 + j, 1 + k, -1 + n] + aux[1 + i, j, -1 + k, -1 + n] + aux[1 + i, 1 + j, -1 + 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: A148831 A029892 A148832 * A210680 A121650 A151462

Adjacent sequences: A148830 A148831 A148832 * A148834 A148835 A148836

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved