A151161 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), (0, 1, 0), (0, 1, 1), (1, 0, 1), (1, 1, -1)}.

1, 3, 11, 47, 213, 985, 4676, 22425, 108480, 528613, 2586817, 12707610, 62610096, 309143709, 1529340026, 7576840370, 37583562825, 186620107114, 927438209948, 4612379199847, 22952638529393, 114279053572676, 569242832080266, 2836602158992699, 14139917160801641, 70505804333290276, 351654620617541100

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, -1 + k, -1 + n] + aux[i, -1 + j, -1 + k, -1 + n] + aux[i, -1 + j, 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: A055731 A151159 A151160 * A227846 A124890 A301770

Adjacent sequences: A151158 A151159 A151160 * A151162 A151163 A151164

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved