A149466 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, 1, -1), (1, 0, 1), (1, 1, -1)}.

1, 1, 4, 13, 53, 204, 874, 3723, 16387, 72446, 326215, 1477841, 6760897, 31103660, 144014155, 669926435, 3130656530, 14684820342, 69123314399, 326358901691, 1545191603268, 7334139382820, 34890634801128, 166330881788243, 794451991099846, 3801247637866928, 18217657255955808, 87440714019506163

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, -1 + 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: A151476 A140454 A149465 * A369226 A006604 A082570

Adjacent sequences: A149463 A149464 A149465 * A149467 A149468 A149469

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved