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A057606
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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)).
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2
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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
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3,1
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COMMENTS
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Row lengths = 2^(n-2), row sums = 2^n.
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REFERENCES
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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.
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LINKS
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EXAMPLE
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2,6; 2,4,6,4; 2,4,8,4,8,4,2,0; ...
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PROG
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(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)
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CROSSREFS
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KEYWORD
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nonn,tabf,nice
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AUTHOR
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STATUS
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approved
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