A098744 - OEIS

A098744

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.

%I #14 Dec 18 2019 02:03:23

%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 Reed-Muller 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