

A057606


Triangle read by rows: T(n,k) = number of binary ntuples u having exactly k grandchildren, where a grandchild is a vector obtained by deleting any two coordinates of u (n >= 3, 1<=k<=2^(n2)).


2



2, 6, 2, 4, 6, 4, 2, 4, 8, 4, 8, 4, 2, 0, 2, 4, 10, 6, 12, 8, 8, 6, 6, 0, 2, 0, 0, 0, 0, 0, 2, 4, 12, 8, 16, 14, 16, 12, 12, 12, 6, 4, 8, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 4, 14, 10, 20, 22, 24, 22, 22, 26, 18, 16, 12, 16, 12, 0, 4, 10, 0, 0, 0, 2, 0, 0, 0, 0
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OFFSET

3,1


COMMENTS

Row lengths = 2^(n2), row sums = 2^n.


REFERENCES

N. J. A. Sloane, On singledeletioncorrecting codes, in Codes and Designs (Columbus, OH, 2000), 273291, Ohio State Univ. Math. Res. Inst. Publ., 10, de Gruyter, Berlin, 2002.


LINKS



EXAMPLE

2,6; 2,4,6,4; 2,4,8,4,8,4,2,0; ...


PROG

(Haskell)
import Data.List (group, sort, nub, inits, tails)
a057606 n k = a057606_tabf !! (n3) !! (k1)
a057606_row n = a057606_tabf !! (n3)
a057606_tabf = map g $ drop 3 $
iterate (\xs > (map (0 :) xs) ++ (map (1 :) xs)) [[]] where
g xss = map length $ fill0 $ group $ sort $ map (length . del2) xss
where fill0 uss = f0 uss [1 .. length xss `div` 4] where
f0 _ [] = []
f0 [] (j:js) = [] : f0 [] js
f0 vss'@(vs:vss) (j:js)
 j == head vs = vs : f0 vss js
 otherwise = [] : f0 vss' js
del2 = nub . (concatMap del1) . del1
del1 xs = nub $
zipWith (++) (init $ inits xs) (map tail $ init $ tails xs)


CROSSREFS



KEYWORD

nonn,tabf,nice


AUTHOR



STATUS

approved



