A127779 - OEIS

A127779

Triangle read by rows: A004736 * A127773.

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, ...).

From Clark Kimberling, Sep 16 2008: (Start)

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 n-th 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

Table of n, a(n) for n=1..45.

Quora, How many triangles are in this picture?.

FORMULA

A004736 * A127773 as infinite lower triangular matrices.

EXAMPLE

First few rows of the triangle:

2, 3;

3, 6, 6;

4, 9, 12, 10;

5, 12, 18, 20, 15;

6, 15, 24, 30, 30, 21;