A150182 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, 0, 1), (0, -1, 1), (0, 1, 0), (1, 0, 0), (1, 1, -1)}.

1, 2, 6, 20, 78, 316, 1356, 5954, 26866, 123102, 572542, 2690656, 12760224, 60945894, 292847054, 1414148872, 6857590976, 33372997268, 162906627036, 797295705256, 3910947686678, 19222025434142, 94637259018346, 466637644814786, 2303954154607022, 11388789655469310, 56355128333046294, 279120481287179976

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, -1 + j, 1 + k, -1 + n] + aux[-1 + i, j, k, -1 + n] + aux[i, -1 + j, k, -1 + n] + aux[i, 1 + j, -1 + k, -1 + n] + aux[1 + i, 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: A150180 A370947 A150181 * A098469 A081563 A038393

Adjacent sequences: A150179 A150180 A150181 * A150183 A150184 A150185

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved