A253586 The sum of the i-th ternary digits of n, k, and A(n,k) equals 0 (mod 3) for each i>=0 (leading zeros included); square array A(n,k), n>=0, k>=0, read by antidiagonals.

0, 2, 2, 1, 1, 1, 6, 0, 0, 6, 8, 8, 2, 8, 8, 7, 7, 7, 7, 7, 7, 3, 6, 6, 3, 6, 6, 3, 5, 5, 8, 5, 5, 8, 5, 5, 4, 4, 4, 4, 4, 4, 4, 4, 4, 18, 3, 3, 0, 3, 3, 0, 3, 3, 18, 20, 20, 5, 2, 2, 5, 2, 2, 5, 20, 20, 19, 19, 19, 1, 1, 1, 1, 1, 1, 19, 19, 19, 24, 18, 18, 24, 0, 0, 6, 0, 0, 24, 18, 18, 24

Offset: 0

Author

Alois P. Heinz, Jan 04 2015

Keywords

• nonn
• base
• tabl
• look

Examples

			Square array A(n,k) begins:
  0, 2, 1, 6, 8, 7, 3, 5, 4, ...
  2, 1, 0, 8, 7, 6, 5, 4, 3, ...
  1, 0, 2, 7, 6, 8, 4, 3, 5, ...
  6, 8, 7, 3, 5, 4, 0, 2, 1, ...
  8, 7, 6, 5, 4, 3, 2, 1, 0, ...
  7, 6, 8, 4, 3, 5, 1, 0, 2, ...
  3, 5, 4, 0, 2, 1, 6, 8, 7, ...
  5, 4, 3, 2, 1, 0, 8, 7, 6, ...
  4, 3, 5, 1, 0, 2, 7, 6, 8, ...
		

Links

• Alois P. Heinz, Antidiagonals n = 0..200, flattened
• Rémy Sigrist, Colored representation of the table for 0 <= n, k < 3^7 (where the hue is function of T(n, k))
• Wikipedia, Set (game)

Crossrefs

Column k=0 and row n=0 gives A004488.

Main diagonal gives A001477.

A(n,floor(n/3)) gives A060587.

Cf. A090245, A253587.

Programs

Maple

A:= proc(n, k) local i, j; `if`(n=0 and k=0, 0,
      A(iquo(n, 3, 'i'), iquo(k, 3, 'j'))*3 +irem(6-i-j, 3))
    end:
seq(seq(A(n, d-n), n=0..d), d=0..14);

Formula

A(n,k) = A(floor(n/3),floor(k/3))*3+(6-(n mod 3)-(k mod 3) mod 3), A(0,0) = 0.