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%I #19 Apr 08 2023 04:45:47
%S 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 42,28,8,21,36,50,60,63,56,36,9,24,42,60,75,84,84,72,45
%N Triangle read by rows: A004736 * A127773.
%C Row sums = bin(n,4), (A000332): (1, 5, 15, 35, ...).
%C From _Clark Kimberling_, Sep 16 2008: (Start)
%C As a rectangular array: R = A000027*A000217; R(m,n) = n*binomial(m+1,2).
%C R is the accumulation array (cf. A144112) of A002260 (rectangular, with n-th row (n,n,n,n,...). (End)
%C 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 Quora, <a href="https://www.quora.com/How-many-triangles-are-in-this-picture-1">How many triangles are in this picture?</a>.
%F A004736 * A127773 as infinite lower triangular matrices.
%e First few rows of the triangle:
%e 1;
%e 2, 3;
%e 3, 6, 6;
%e 4, 9, 12, 10;
%e 5, 12, 18, 20, 15;
%e 6, 15, 24, 30, 30, 21;
%e 7, 18, 30, 40, 45, 42, 28;
%e ...
%e First few rows of the rectangular array:
%e 1 3 6 10 15 ...
%e 2 6 12 20 30 ...
%e 3 9 18 30 45 ...
%e 4 12 24 40 60 ...
%e 5 15 30 50 75 ...
%e ...
%Y Cf. A004736, A127773, A000217, A000332.
%Y Cf. A002260. - _Clark Kimberling_, Sep 16 2008
%K nonn,tabl
%O 1,2
%A _Gary W. Adamson_, Jan 28 2007
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