A149051 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, 1, 1), (1, -1, 1), (1, 1, -1)}.

1, 1, 3, 10, 39, 151, 635, 2658, 11572, 50877, 227745, 1027822, 4690045, 21555194, 99723136, 463989132, 2170140534, 10192764711, 48060915369, 227407643656, 1079360842009, 5136933221246, 24510436767042, 117217482663014, 561731089733592, 2697053390820434, 12972299041925345, 62494501152902793

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, 1 + j, -1 + k, -1 + n] + aux[i, -1 + 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: A149049 A149050 A300974 * A151064 A151065 A151066

Adjacent sequences: A149048 A149049 A149050 * A149052 A149053 A149054

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved