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

0,2

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)

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.

Example

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, ...

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);

Crossrefs

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

Main diagonal gives A001477.

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

Cf. A090245, A253587.

Sequence in context: A180264 A225200 A128706 * A347621 A318191 A208183

Adjacent sequences: A253583 A253584 A253585 * A253587 A253588 A253589

Keyword

nonn,base,tabl,look

Author

Alois P. Heinz, Jan 04 2015

Status

approved