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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.

%I A333286 #21 Aug 31 2021 04:37:31
%S A333286 4,7,7,9,14,9,11,24,24,11,13,30,38,30,13,15,38,60,60,38,15,17,44,76,
%T A333286 86,76,44,17,19,52,92,120,120,92,52,19,21,58,106,146,158,146,106,58,
%U A333286 21,23,66,126,178,216,216,178,126,66,23,25,72,142,206,264,278
%N 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.
%C A333286 This was originally based on the data in _Jinyuan Wang_'s A324042, and then extended by _Lars Blomberg_.
%C A333286 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 A333286 Lars Blomberg, <a href="/A333286/b333286.txt">Table of n, a(n) for n = 1..3240 (the first 80 rows)</a>
%H A333286 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 A333286 Triangle begins:
%e A333286 4,
%e A333286 7,  7,
%e A333286 9, 14,  9,
%e A333286 11, 24, 24, 11,
%e A333286 13, 30, 38, 30, 13,
%e A333286 15, 38, 60, 60, 38, 15,
%e A333286 17, 44, 76, 86, 76, 44, 17,
%e A333286 ...
%Y A333286 Cf. A306302, A331452, A324042, A324043, A333287, A333288.
%K A333286 nonn,tabl
%O A333286 1,1
%A A333286 _N. J. A. Sloane_, Mar 20 2020
%E A333286 a(29) and beyond from _Lars Blomberg_, Apr 23 2020