A150236 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, 0, 1), (0, 1, 0), (1, 0, -1), (1, 0, 1)}.

1, 2, 6, 22, 82, 334, 1380, 5872, 25544, 112138, 500750, 2252154, 10222930, 46762182, 215003456, 994846044, 4622431714, 21571568870, 101058672192, 474916738396, 2239134835624, 10584652394092, 50162409675976, 238282808508786, 1134205618874066, 5409558426362536, 25846083437525434, 123695512593180830

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[-1 + i, j, 1 + k, -1 + n] + aux[i, -1 + j, k, -1 + n] + aux[1 + i, 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: A150233 A150234 A150235 * A068946 A150237 A122449

Adjacent sequences: A150233 A150234 A150235 * A150237 A150238 A150239

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved