|
%I #38 Jan 14 2023 09:55:26
%S 13,37,99,213,401,657,1085,1619,2327,3257,4457,5883,7751,9885,12403,
%T 15513,19131,23181,28115,33601,39745,46821,54865,63733,73879,84889,
%U 97063,110639,125649,141797,160129,179981,201175,224481,249403,276291,306003,337425
%N Number of vertices formed by drawing the lines connecting any two of the 2*(n+2) perimeter points of a 3 X (n+1) rectangular grid of points (or equally, a 2 X n grid of squares).
%C Triangles A331452, A331453, A331454 do not have formulas, except for column 1. The column 2 sequences, A331763, A331765, A331766, are therefore the next ones to attack.
%C See A331452 for other illustrations.
%H Lars Blomberg, <a href="/A331763/b331763.txt">Table of n, a(n) for n = 1..100</a>
%H 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>, (2020). Also arXiv:2009.07918.
%H Scott R. Shannon, <a href="/A331452/a331452_13.png">Colored illustration for a(3) = 99</a>
%H Scott R. Shannon, <a href="/A331452/a331452_1.txt">Data specifically for nX2 (or 2Xn) rectangles</a>
%H N. J. A. Sloane (in collaboration with Scott R. Shannon), <a href="/A331452/a331452.pdf">Art and Sequences</a>, Slides of guest lecture in Math 640, Rutgers Univ., Feb 8, 2020. Mentions this sequence.
%H N. J. A. Sloane, <a href="https://arxiv.org/abs/2301.03149">"A Handbook of Integer Sequences" Fifty Years Later</a>, arXiv:2301.03149 [math.NT], 2023, p. 20.
%Y Column 2 of A331453.
%Y Cf. A331765, A331766, A331767.
%K nonn
%O 1,1
%A _Scott R. Shannon_ and _N. J. A. Sloane_, Feb 05 2020
%E More terms from _Scott R. Shannon_, Mar 11 2020
%E a(21) and beyond from _Lars Blomberg_, Apr 28 2020
|
