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 A127779 #22 Jan 26 2025 20:26:49 %S A127779 1,2,3,3,6,6,4,9,12,10,5,12,18,20,15,6,15,24,30,30,21,7,18,30,40,45, %T A127779 42,28,8,21,36,50,60,63,56,36,9,24,42,60,75,84,84,72,45 %N A127779 Triangle read by rows: A004736 * A127773. %C A127779 Row sums = bin(n,4), (A000332): (1, 5, 15, 35, ...). %C A127779 From _Clark Kimberling_, Sep 16 2008: (Start) %C A127779 As a rectangular array: R = A000027*A000217; R(m,n) = n*binomial(m+1,2). %C A127779 R is the accumulation array (cf. A144112) of A002260 (rectangular, with n-th row (n,n,n,n,...)). (End) %C A127779 As a rectangular array read by ascending antidiagonals, T(n,k) is the total number of triangles obtained when a triangle is cut into n parts with segments going down from the apex to its base and into k parts with segments parallel to its base. See Quora link. - _Michel Marcus_, Apr 07 2023 %H A127779 Quora, <a href="https://www.quora.com/How-many-triangles-are-in-this-picture-1">How many triangles are in this picture?</a>. %F A127779 A004736 * A127773 as infinite lower triangular matrices. %e A127779 First few rows of the triangle: %e A127779 1; %e A127779 2, 3; %e A127779 3, 6, 6; %e A127779 4, 9, 12, 10; %e A127779 5, 12, 18, 20, 15; %e A127779 6, 15, 24, 30, 30, 21; %e A127779 7, 18, 30, 40, 45, 42, 28; %e A127779 ... %e A127779 First few rows of the rectangular array: %e A127779 1 3 6 10 15 ... %e A127779 2 6 12 20 30 ... %e A127779 3 9 18 30 45 ... %e A127779 4 12 24 40 60 ... %e A127779 5 15 30 50 75 ... %e A127779 ... %Y A127779 Cf. A004736, A127773, A000217, A000332. %Y A127779 Cf. A002260. - _Clark Kimberling_, Sep 16 2008 %K A127779 nonn,tabl %O A127779 1,2 %A A127779 _Gary W. Adamson_, Jan 28 2007