A150180 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, 1, -1), (0, 1, 1), (1, -1, -1), (1, 0, 1)}.

1, 2, 6, 20, 78, 294, 1232, 5054, 22030, 94440, 422108, 1860772, 8464620, 38065850, 175367844, 800356552, 3723096760, 17182360742, 80544863800, 375031606144, 1768897009760, 8295744867688, 39327988575160, 185529878229380, 883330052851440, 4187776470485006, 20011227976481174, 95271191591075352

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, 1 + j, 1 + k, -1 + n] + aux[i, -1 + j, -1 + k, -1 + n] + aux[1 + i, -1 + 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: A150177 A150178 A150179 * A370947 A150181 A150182

Adjacent sequences: A150177 A150178 A150179 * A150181 A150182 A150183

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved