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A333287 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 quadrilateral regions in the k-th rectangle.

%I A333287 #24 Aug 31 2021 04:37:41
%S A333287 0,1,1,3,8,3,5,12,12,5,7,22,32,22,7,9,28,40,40,28,9,11,38,58,74,58,38,
%T A333287 11,13,46,74,98,98,74,46,13,15,58,92,130,152,130,92,58,15,17,68,104,
%U A333287 150,180,180,150,104,68,17,19,82,124,180,224,254,224,180,124,82,19
%N A333287 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 quadrilateral regions in the k-th rectangle.
%C A333287 This was originally based on the data in _Jinyuan Wang_'s A324042, and then extended by _Lars Blomberg_.
%C A333287 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.
%H A333287 Lars Blomberg, <a href="/A333287/b333287.txt">Table of n, a(n) for n = 1..3240 (the first 80 rows)</a>
%H A333287 Lars Blomberg, Scott R. Shannon and N. J. A. Sloane, <a href="http://neilsloane.com/doc/rose_5.pdf">Graphical Enumeration and Stained Glass Windows, 1: Rectangular Grids</a>, (2021). Also arXiv:2009.07918.
%e A333287 Triangle begins:
%e A333287 0,
%e A333287 1,  1,
%e A333287 3,  8,  3,
%e A333287 5, 12, 12,  5,
%e A333287 7, 22, 32, 22,  7,
%e A333287 9, 28, 40, 40, 28,  9,
%e A333287 11, 38, 58, 74, 58, 38, 11,
%e A333287 ...
%Y A333287 Cf. A306302, A331452, A324042, A324043, A333286, A333288.
%K A333287 nonn,tabl
%O A333287 1,4
%A A333287 _N. J. A. Sloane_, Mar 20 2020
%E A333287 a(29) and beyond from _Lars Blomberg_, Apr 23 2020