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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
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified June 20 17:43 EDT 2021. Contains 345199 sequences. (Running on oeis4.)