



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, 42, 28, 8, 21, 36, 50, 60, 63, 56, 36, 9, 24, 42, 60, 75, 84, 84, 72, 45
(list;
table;
graph;
refs;
listen;
history;
text;
internal format)



OFFSET

1,2


COMMENTS

Row sums = bin(n,4), (A000332): (1, 5, 15, 35, ...).
As a rectangular array: R = A000027*A000217; R(m,n) = n*binomial(m+1,2).
R is the accumulation array (cf. A144112) of A002260 (rectangular, with nth row (n,n,n,n,...). (End)
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


LINKS



FORMULA



EXAMPLE

First few rows of the triangle:
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, 42, 28;
...
First few rows of the rectangular array:
1 3 6 10 15 ...
2 6 12 20 30 ...
3 9 18 30 45 ...
4 12 24 40 60 ...
5 15 30 50 75 ...
...


CROSSREFS



KEYWORD



AUTHOR



STATUS

approved



