A150850 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, 0), (0, -1, 1), (1, 0, -1), (1, 0, 0), (1, 1, 1)}.

1, 2, 8, 32, 140, 624, 2835, 13083, 60972, 286915, 1358879, 6471544, 30958497, 148639296, 715975304, 3458054422, 16742032860, 81223525103, 394774557700, 1921859283853, 9369609275641, 45739130217128, 223544562299062, 1093714600090306, 5356310718357100, 26255094806635557, 128799993599104739

Offset

0,2

Links

Table of n, a(n) for n=0..26.

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[-1 + i, j, 1 + k, -1 + n] + aux[i, 1 + j, -1 + k, -1 + n] + aux[1 + i, 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: A150847 A150848 A150849 * A179469 A150851 A150852

Adjacent sequences: A150847 A150848 A150849 * A150851 A150852 A150853

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved