Voozh

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

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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:

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)