%I
%S 1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,1,1,1,1,1,1,1,1,2,2,3,3,4,3,3,2,2,1,1,
%T 1,1,1,1,1,1,2,2,4,5,8,9,15,16,23,24,30,30,38,30,30,24,23,16,15,9,8,5,
%U 4,2,2,1,1,1,1
%N Triangle read by rows: row n gives the number of orbits of the group GA(n) acting on binary vectors of length 2^n and weight k, for n >= 0, 0 <= k <= 2^n.
%C GA(n) is the general affine group, the automorphism group of the ReedMuller code RM(r,n).
%C Since the group is triply transitive, there's only one orbit for vectors of weight 0,1,2,3.
%e Triangle begins:
%e 1 1
%e 1 1 1
%e 1 1 1 1 1
%e 1 1 1 1 2 1 1 1 1 (the 2 is because there are two orbits on vectors of length 8 and weight 4)
%e 1 1 1 1 2 2 3 3 4 3 3 2 2 1 1 1 1
%Y Cf. A000214 (row sums).  _Vladeta Jovovic_, Feb 22 2009
%K nonn,tabf,more
%O 0,15
%A Alexander Vardy (avardy(AT)ucsd.edu), Nov 15 2008
%E More terms from _Vladeta Jovovic_, Feb 22 2009
