A148340 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), (-1, 0, -1), (0, 1, 1), (1, 0, -1)}.

1, 1, 2, 5, 15, 38, 126, 403, 1279, 4376, 15361, 52102, 188609, 680752, 2450641, 9089379, 33719262, 125430770, 475968218, 1796731739, 6849544648, 26396870678, 101253870085, 392467382251, 1531000530315, 5952481787141, 23368070361558, 91997443972187, 361899755511914, 1434849012341938, 5692008006992570

Offset

0,3

Links

Table of n, a(n) for n=0..30.

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[1 + i, 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: A034522 A276720 A148339 * A148341 A258121 A242823

Adjacent sequences: A148337 A148338 A148339 * A148341 A148342 A148343

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved