cp's OEIS Frontend

A333288 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 regions in the k-th rectangle.

%I A333288 #27 Aug 31 2021 04:37:49
%S A333288 4,8,8,12,22,12,16,36,36,16,20,52,70,52,20,24,66,100,100,66,24,28,82,
%T A333288 134,160,134,82,28,32,98,166,218,218,166,98,32,36,116,198,276,310,276,
%U A333288 198,116,36,40,134,230,328,396,396,328,230,134,40,44,154,266,386
%N A333288 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 regions in the k-th rectangle.
%C A333288 This was originally based on the data in _Jinyuan Wang_'s A324042, and then extended by _Lars Blomberg_.
%C A333288 Since the cells are either triangles or quadrilaterals, this is the sum of the two arrays A333286 and A333287.
%C A333288 It would be nice to have a formula for these entries. It is easy to see that the first column is 4n for n>=1.
%H A333288 Lars Blomberg, <a href="/A333288/b333288.txt">Table of n, a(n) for n = 1..3240 (the first 80 rows)</a>
%H A333288 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 A333288 Triangle begins:
%e A333288    4;
%e A333288    8,   8;
%e A333288   12,  22,  12;
%e A333288   16,  36,  36,  16;
%e A333288   20,  52,  70,  52,  20;
%e A333288   24,  66, 100, 100,  66,  24;
%e A333288   28,  82, 134, 160, 134,  82,  28;
%e A333288   ...
%Y A333288 Cf. A306302, A331452, A324042, A324043, A333286, A333287, A333288, A335056, A335074.
%K A333288 nonn,tabl
%O A333288 1,1
%A A333288 _N. J. A. Sloane_, Mar 20 2020
%E A333288 a(29) and beyond from _Lars Blomberg_, Apr 23 2020