A253587 The sum of the i-th ternary digits of n, k, and T(n,k) equals 0 (mod 3) for each i>=0 (leading zeros included); triangle T(n,k), n>=0, 0<=k<=n, read by rows.

0, 2, 1, 1, 0, 2, 6, 8, 7, 3, 8, 7, 6, 5, 4, 7, 6, 8, 4, 3, 5, 3, 5, 4, 0, 2, 1, 6, 5, 4, 3, 2, 1, 0, 8, 7, 4, 3, 5, 1, 0, 2, 7, 6, 8, 18, 20, 19, 24, 26, 25, 21, 23, 22, 9, 20, 19, 18, 26, 25, 24, 23, 22, 21, 11, 10, 19, 18, 20, 25, 24, 26, 22, 21, 23, 10, 9, 11

Offset: 0

Author

Alois P. Heinz, Jan 04 2015

Keywords

• nonn
• base
• tabl
• look

Examples

			Triangle T(n,k) begins:
  0;
  2, 1;
  1, 0, 2;
  6, 8, 7, 3;
  8, 7, 6, 5, 4;
  7, 6, 8, 4, 3, 5;
  3, 5, 4, 0, 2, 1, 6;
  5, 4, 3, 2, 1, 0, 8, 7;
  4, 3, 5, 1, 0, 2, 7, 6, 8;
		

Links

• Alois P. Heinz, Rows n = 0..200, flattened
• Wikipedia, Set (game)

Crossrefs

Column k=0 gives A004488.

Main diagonal gives A001477.

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

Cf. A090245, A253586.

Programs

Maple

T:= proc(n, k) local i, j; `if`(n=0 and k=0, 0,
      T(iquo(n, 3, 'i'), iquo(k, 3, 'j'))*3 +irem(6-i-j, 3))
    end:
seq(seq(T(n, k), k=0..n), n=0..14);

Formula

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