A150759 - OEIS

A150759

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, 0), (-1, 0, 0), (0, 0, -1), (0, 0, 1), (1, 1, 1)}

%I #2 Mar 30 2012 18:54:23

%S 1,2,8,30,120,504,2126,9170,40044,176044,781600,3490012,15664056,

%T 70669628,320004610,1454279906,6630320468,30309488628,138910831512,

%U 638073465476,2936860540160,13543141717064,62559629953436,289436485560372,1341060883889256,6221966893608856,28903711416385792,134427762081030024

%N 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, 0), (-1, 0, 0), (0, 0, -1), (0, 0, 1), (1, 1, 1)}

%H A. Bostan and M. Kauers, 2008. Automatic Classification of Restricted Lattice Walks, <a href="http://arxiv.org/abs/0811.2899">ArXiv 0811.2899</a>.

%t 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[i, j, -1 + k, -1 + n] + aux[i, j, 1 + k, -1 + n] + aux[1 + i, j, k, -1 + n] + aux[1 + i, 1 + j, k, -1 + n]]; Table[Sum[aux[i, j, k, n], {i, 0, n}, {j, 0, n}, {k, 0, n}], {n, 0, 10}]

%K nonn,walk

%O 0,2

%A _Manuel Kauers_, Nov 18 2008