This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A379777 #10 Jan 04 2025 11:07:18
%S A379777 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,
%T A379777 16,12,9,13,17,22,28,28,22,17,13,14,18,23,29,36,36,29,23,18,14,19,24,
%U A379777 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
%N 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.
%C A379777 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.
%C A379777 This square array combines two symetrical copies of the triangular view of A001477 (the nonnegative integers):
%C A379777 0 1 3 6 .
%C A379777 2 4 7 . 0 1 3 6 .
%C A379777 5 8 . 0 2 4 7 .
%C A379777 0 9 . -> 1 2 5 8 .
%C A379777 1 2 . 3 4 5 9 .
%C A379777 3 4 5 6 7 8 9 .
%C A379777 6 7 8 9 . . . . .
%C A379777 . . . . .
%H A379777 Rémy Sigrist, <a href="/A379777/b379777.txt">Table of n, a(n) for n = 0..10010</a>
%H A379777 Wikipedia, <a href="https://en.wikipedia.org/wiki/Dobble">Dobble</a>
%F A379777 A(0, k) = A000217(k).
%F A379777 A(n, k) = A(k+1, n) = A000217(k) + n for any n in 0..k.
%F A379777 A(n, n) = A000096(n).
%e A379777 Array A(n, k) begins:
%e A379777 n\k | 0 1 2 3 4 5 6 7 8 9
%e A379777 ----+---------------------------------------
%e A379777 0 | 0 1 3 6 10 15 21 28 36 45
%e A379777 1 | 0 2 4 7 11 16 22 29 37 46
%e A379777 2 | 1 2 5 8 12 17 23 30 38 47
%e A379777 3 | 3 4 5 9 13 18 24 31 39 48
%e A379777 4 | 6 7 8 9 14 19 25 32 40 49
%e A379777 5 | 10 11 12 13 14 20 26 33 41 50
%e A379777 6 | 15 16 17 18 19 20 27 34 42 51
%e A379777 7 | 21 22 23 24 25 26 27 35 43 52
%e A379777 8 | 28 29 30 31 32 33 34 35 44 53
%e A379777 9 | 36 37 38 39 40 41 42 43 44 54
%e A379777 10 | 45 46 47 48 49 50 51 52 53 54
%o A379777 (PARI) A(n, k) = { my (x, y); if (n > k, x = n-1; y = k, x = k; y = n;); x*(x+1)/2 + y }
%Y A379777 Cf. A000096, A000217, A001477, A002024, A002262.
%K A379777 nonn,tabl,easy
%O A379777 0,5
%A A379777 _Rémy Sigrist_, Jan 02 2025