A374560 Square array A(n, k), n, k >= 0, read by antidiagonals; A(n, k) = A005836(n+1) + A005836(k+1).

0, 1, 1, 3, 2, 3, 4, 4, 4, 4, 9, 5, 6, 5, 9, 10, 10, 7, 7, 10, 10, 12, 11, 12, 8, 12, 11, 12, 13, 13, 13, 13, 13, 13, 13, 13, 27, 14, 15, 14, 18, 14, 15, 14, 27, 28, 28, 16, 16, 19, 19, 16, 16, 28, 28, 30, 29, 30, 17, 21, 20, 21, 17, 30, 29, 30, 31, 31, 31, 31, 22, 22, 22, 22, 31, 31, 31, 31

Offset: 0

Author

Rémy Sigrist, Jul 20 2024

Keywords

• nonn
• base
• tabl
• easy

Comments

For any v >= 0, the value v appears A120880(v) times.

Examples

			Array A(n, k) begins:
  n\k |  0   1   2   3   4   5   6   7   8   9  10  11  12
  ----+---------------------------------------------------
    0 |  0   1   3   4   9  10  12  13  27  28  30  31  36
    1 |  1   2   4   5  10  11  13  14  28  29  31  32  37
    2 |  3   4   6   7  12  13  15  16  30  31  33  34  39
    3 |  4   5   7   8  13  14  16  17  31  32  34  35  40
    4 |  9  10  12  13  18  19  21  22  36  37  39  40  45
    5 | 10  11  13  14  19  20  22  23  37  38  40  41  46
    6 | 12  13  15  16  21  22  24  25  39  40  42  43  48
    7 | 13  14  16  17  22  23  25  26  40  41  43  44  49
    8 | 27  28  30  31  36  37  39  40  54  55  57  58  63
    9 | 28  29  31  32  37  38  40  41  55  56  58  59  64
   10 | 30  31  33  34  39  40  42  43  57  58  60  61  66
   11 | 31  32  34  35  40  41  43  44  58  59  61  62  67
   12 | 36  37  39  40  45  46  48  49  63  64  66  67  72
		

Links

• Rémy Sigrist, Table of n, a(n) for n = 0..8255 (antidiagonals for n+k = 0..127 flattened)

Crossrefs

Cf. A005836, A120880, A374789, A374790, A374791, A374792.

Programs

PARI

A(n, k) = fromdigits(binary(n), 3) + fromdigits(binary(k), 3)

Formula

A(n, k) = A(k, n).

A(2*n, 2*k) = 3*A(n, k).