A057606 Triangle read by rows: T(n,k) = number of binary n-tuples u having exactly k grandchildren, where a grandchild is a vector obtained by deleting any two coordinates of u (n >= 3, 1<=k<=2^(n-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

Offset

3,1

Comments

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

References

N. J. A. Sloane, On single-deletion-correcting codes, in Codes and Designs (Columbus, OH, 2000), 273-291, Ohio State Univ. Math. Res. Inst. Publ., 10, de Gruyter, Berlin, 2002.

Links

Reinhard Zumkeller, Rows n = 3..15 of triangle, flattened

N. J. A. Sloane, On single-deletion-correcting codes

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 !! (n-3) !! (k-1)
a057606_row n = a057606_tabf !! (n-3)
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)
-- Reinhard Zumkeller, Apr 30 2012

Crossrefs

Cf. A057607.

Sequence in context: A151944 A073094 A194953 * A021385 A085193 A220242

Adjacent sequences: A057603 A057604 A057605 * A057607 A057608 A057609

Keyword

nonn,tabf,nice

Author

N. J. A. Sloane, Oct 08 2000

Status

approved