A150184 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, -1, 1), (0, 0, -1), (0, 1, 1), (1, 0, 1)}.

1, 2, 6, 20, 80, 294, 1178, 4720, 19796, 81376, 346368, 1465122, 6331534, 27192882, 118745262, 516568790, 2274700234, 9991853262, 44299962722, 196064059838, 874195069474, 3893785311022, 17444530696426, 78101794611148, 351344326779916, 1580049080320688, 7133376499493764, 32201501988720644

Offset

0,2

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[i, -1 + j, -1 + k, -1 + n] + aux[i, j, 1 + k, -1 + n] + aux[1 + i, 1 + 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: A346747 A300514 A150183 * A150185 A354737 A357502

Adjacent sequences: A150181 A150182 A150183 * A150185 A150186 A150187

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved