A149656 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, 0, 0), (0, 0, -1), (0, 1, -1), (1, 1, 1)}.

1, 1, 5, 17, 53, 233, 909, 3361, 14885, 61241, 242717, 1085329, 4598229, 18926889, 85303757, 368267009, 1552593669, 7041525529, 30802363261, 132037599601, 601853765429, 2658662122505, 11537150940205, 52805458896097, 235044956158053, 1029638420961785, 4728821380317661, 21177107496077649

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[i, -1 + j, 1 + k, -1 + n] + aux[i, j, 1 + k, -1 + n] + aux[1 + i, 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: A178828 A242429 A097160 * A146063 A146006 A161470

Adjacent sequences: A149653 A149654 A149655 * A149657 A149658 A149659

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved