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 A248971 #11 Sep 08 2022 08:46:10
%S A248971 0,1,3,2,6,4,10,7,6,15,11,9,21,16,13,12,28,22,18,16,36,29,24,21,20,45,
%T A248971 37,31,27,25,55,46,39,34,31,30,66,56,48,42,38,36,78,67,58,51,46,43,42,
%U A248971 91,79,69,61,55,51,49,105,92,81,72,65,60,57,56
%N A248971 Triangular array read by rows. T(n,k)=C(k,2)+C(n-k,2),n>=2,1<=k<=floor(n/2).
%C A248971 G is a simple graph of order n with exactly 2 components each of which is complete. T(n,k) is the total number of edges in G when one component contains exactly k vertices.
%e A248971 0,
%e A248971 1,
%e A248971 3, 2,
%e A248971 6, 4,
%e A248971 10, 7, 6,
%e A248971 15, 11, 9,
%e A248971 21, 16, 13, 12,
%e A248971 28, 22, 18, 16,
%e A248971 36, 29, 24, 21, 20
%t A248971 Table[Table[Binomial[k, 2] + Binomial[n - k, 2], {k, 1, n/2}], {n, 2,
%t A248971 10}] // Grid
%o A248971 (Magma) [Binomial(k,2)+Binomial(n-k,2): k in [1..Floor(n/2)], n in [1..16]]; // _Vincenzo Librandi_, Oct 19 2014
%Y A248971 Cf. A000217 (column 1), A000124 (column 2), A152950 (column 3), A002620 (row ends).
%K A248971 nonn,tabf
%O A248971 2,3
%A A248971 _Geoffrey Critzer_, Oct 18 2014