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

0,2

Links

Alois P. Heinz, Rows n = 0..200, flattened

Wikipedia, Set (game)

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.

Example

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;

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);

Crossrefs

Column k=0 gives A004488.

Main diagonal gives A001477.

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

Cf. A090245, A253586.

Sequence in context: A333213 A301636 A238857 * A110962 A065715 A180984

Adjacent sequences: A253584 A253585 A253586 * A253588 A253589 A253590

Keyword

nonn,base,tabl,look

Author

Alois P. Heinz, Jan 04 2015

Status

approved