A379777 Array A(n, k), n, k >= 0, read by upward antidiagonals; for any v >= 0, the value appears twice in the array: in row A002262(v) and in row A002024(v+1); values in each row are given in strictly increasing order.

0, 0, 1, 1, 2, 3, 3, 2, 4, 6, 6, 4, 5, 7, 10, 10, 7, 5, 8, 11, 15, 15, 11, 8, 9, 12, 16, 21, 21, 16, 12, 9, 13, 17, 22, 28, 28, 22, 17, 13, 14, 18, 23, 29, 36, 36, 29, 23, 18, 14, 19, 24, 30, 37, 45, 45, 37, 30, 24, 19, 20, 25, 31, 38, 46, 55, 55, 46, 38, 31, 25, 20, 26, 32, 39, 47, 56, 66

Offset

0,5

Comments

This sequence was inspired by the game Dobble: this game is based on cards with symbols such that two distinct cards always have exactly one common symbol. Here, two distinct rows have exactly one common term.

This square array combines two symetrical copies of the triangular view of A001477 (the nonnegative integers):

0 1 3 6 .

2 4 7 . 0 1 3 6 .

5 8 . 0 2 4 7 .

0 9 . -> 1 2 5 8 .

1 2 . 3 4 5 9 .

3 4 5 6 7 8 9 .

6 7 8 9 . . . . .

. . . . .

Links

Rémy Sigrist, Table of n, a(n) for n = 0..10010

Wikipedia, Dobble

Formula

A(0, k) = A000217(k).

A(n, k) = A(k+1, n) = A000217(k) + n for any n in 0..k.

A(n, n) = A000096(n).

Example

Array A(n, k) begins:
  n\k |  0   1   2   3   4   5   6   7   8   9
  ----+---------------------------------------
    0 |  0   1   3   6  10  15  21  28  36  45
    1 |  0   2   4   7  11  16  22  29  37  46
    2 |  1   2   5   8  12  17  23  30  38  47
    3 |  3   4   5   9  13  18  24  31  39  48
    4 |  6   7   8   9  14  19  25  32  40  49
    5 | 10  11  12  13  14  20  26  33  41  50
    6 | 15  16  17  18  19  20  27  34  42  51
    7 | 21  22  23  24  25  26  27  35  43  52
    8 | 28  29  30  31  32  33  34  35  44  53
    9 | 36  37  38  39  40  41  42  43  44  54
   10 | 45  46  47  48  49  50  51  52  53  54

Prog

(PARI) A(n, k) = { my (x, y); if (n > k, x = n-1; y = k, x = k; y = n; ); x*(x+1)/2 + y }

Crossrefs

Cf. A000096, A000217, A001477, A002024, A002262.

Sequence in context: A131469 A309076 A393434 * A343326 A073078 A360296

Adjacent sequences: A379774 A379775 A379776 * A379778 A379779 A379780

Keyword

nonn,tabl,easy

Author

Rémy Sigrist, Jan 02 2025

Status

approved