A333286 - OEIS

A333286

Triangle read by rows: consider a figure made up of a row of n congruent rectangles and the diagonals of all visible rectangles; T(n,k) (1 <= k <= n) is the number of triangular regions in the k-th rectangle.

4, 7, 7, 9, 14, 9, 11, 24, 24, 11, 13, 30, 38, 30, 13, 15, 38, 60, 60, 38, 15, 17, 44, 76, 86, 76, 44, 17, 19, 52, 92, 120, 120, 92, 52, 19, 21, 58, 106, 146, 158, 146, 106, 58, 21, 23, 66, 126, 178, 216, 216, 178, 126, 66, 23, 25, 72, 142, 206, 264, 278

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OFFSET

1,1

COMMENTS

This was originally based on the data in Jinyuan Wang's A324042, and then extended by Lars Blomberg.

It would be nice to have a formula for these entries. It is easy to see that the first column is 2n+3 for n>1.

LINKS

Lars Blomberg, Table of n, a(n) for n = 1..3240 (the first 80 rows)

Lars Blomberg, Scott R. Shannon and N. J. A. Sloane, Graphical Enumeration and Stained Glass Windows, 1: Rectangular Grids, (2021). Also arXiv:2009.07918.

EXAMPLE

Triangle begins:

7, 7,