A149038 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, 1, 1), (1, -1, 1), (1, 0, -1)}.

1, 1, 3, 10, 35, 135, 541, 2217, 9377, 40349, 175942, 778143, 3477104, 15671149, 71188693, 325532865, 1497282449, 6922353003, 32148253707, 149919105537, 701702507444, 3295012665703, 15519855244683, 73301505108780, 347061046971505, 1647058682479621, 7833160088904523, 37325460274234458

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, j, 1 + k, -1 + n] + aux[-1 + i, 1 + j, -1 + k, -1 + n] + aux[i, -1 + 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: A151047 A008984 A151048 * A097148 A149039 A151477

Adjacent sequences: A149035 A149036 A149037 * A149039 A149040 A149041

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved