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.

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, 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, 4, 2, 2, 1, 1, 1, 1

Offset: 0

Author

Alexander Vardy (avardy(AT)ucsd.edu), Nov 15 2008

Keywords

• nonn
• tabf
• more

Comments

GA(n) is the general affine group, the automorphism group of the Reed-Muller code RM(r,n).

Since the group is triply transitive, there's only one orbit for vectors of weight 0,1,2,3.

Examples

			Triangle begins:
1 1
1 1 1
1 1 1 1 1
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)
1 1 1 1 2 2 3 3 4 3 3 2 2 1 1 1 1
		

Crossrefs

Cf. A000214 (row sums). - Vladeta Jovovic, Feb 22 2009

Extensions

More terms from Vladeta Jovovic, Feb 22 2009