Count the number of Hamming distance sequences
Haskell, score 9

import Data.Bits
import Data.List
import qualified Data.IntSet as S

main = mapM_ (print . S.size . S.fromList . hd) [1..9]

hd :: Int -&gt; [Int]
hd n = [foldl' (\s e-&gt;s*m+e) 0 [popCount $ xor p (shiftR t i .&amp;. m)|i&lt;-[(0::Int)..n-1]] | let m=2^n-1,p&lt;-[(0::Int)..2^n-1],t&lt;-[(0::Int)..2^(2*n-1)-1]]


Compile with -O3. It takes 6min35s on my 6 year old laptop hardware to run up to n=9, so maybe it's under 5min on the reference hardware. 

&gt; time ./113785
2
9
48
297
2040
15425
125232
1070553
9530752

real  6m35.763s
user  6m27.690s
sys   0m5.025s