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

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:
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,
...

Crossrefs

Cf. A306302, A331452, A324042, A324043, A333287, A333288.

Sequence in context: A103711 A199435 A257898 * A159919 A310929 A310930

Adjacent sequences: A333283 A333284 A333285 * A333287 A333288 A333289

Keyword

nonn,tabl

Author

N. J. A. Sloane, Mar 20 2020

Extensions

a(29) and beyond from Lars Blomberg, Apr 23 2020

Status

approved