A057607 Triangle 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 >= 2, 0<=k<=2^(n-2)).

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

Offset

2,1

Comments

Row sums = 2^n. - Sean A. Irvine, Jun 20 2022

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, Table of n, a(n) for n = 2..16397 [a(2) changed by Georg Fischer, Jul 11 2022]

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

Example

Triangle begins:
  4;
  0,2,6;
  0,2,4,6,4;
  0,2,4,8,4,8,4,2,0;
  ...
a(2)=4 because each of 00, 01, 10, 11, leaves no grandchildren. - Sean A. Irvine, Jun 20 2022

Prog

(Haskell)
a057607 n k = a057607_tabf !! (n-2) !! k
a057607_row n = a057607_tabf !! (n-2)
a057607_tabf =  [4] : map (0 :) a057606_tabf
-- Reinhard Zumkeller, Apr 30 2012

Crossrefs

Cf. A057606.

Sequence in context: A016679 A178903 A322259 * A240943 A271823 A011352

Adjacent sequences: A057604 A057605 A057606 * A057608 A057609 A057610

Keyword

nonn,tabf,nice

Author

N. J. A. Sloane, Oct 08 2000

Extensions

a(2) corrected by Sean A. Irvine, Jun 20 2022

Status

approved