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

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:
  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

Cf. A004736, A127773, A000217, A000332.

Cf. A002260. - Clark Kimberling, Sep 16 2008

Sequence in context: A075258 A321745 A212629 * A207634 A222862 A101437

Adjacent sequences: A127776 A127777 A127778 * A127780 A127781 A127782

Keyword

nonn,tabl

Author

Gary W. Adamson, Jan 28 2007

Status

approved