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A331449 a(0) = 1 by convention; for n>0, a(n) is the number of points in the n-th figure shown in A255011 (meaning the figure with 4n points on the perimeter).

%I A331449 #40 Apr 16 2025 19:42:00
%S A331449 1,5,37,257,817,2757,4825,12293,19241,33549,49577,87685,101981,178465,
%T A331449 220113,286357,379097,551669,606241,880293,951445,1209049,1507521,
%U A331449 1947877,2002669,2624409,3056093,3550425,3955049,5069037,5062153,6669665,7081969,8143193,9365089,10296469
%N A331449 a(0) = 1 by convention; for n>0, a(n) is the number of points in the n-th figure shown in A255011 (meaning the figure with 4n points on the perimeter).
%C A331449 Equivalently, this is A334690(n) + 4*n.
%H A331449 Zhao Hui Du, <a href="/A331449/b331449.txt">Table of n, a(n) for n = 0..136</a> (terms 0..52 from Lars Blomberg).
%H A331449 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.
%H A331449 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.
%H A331449 Scott R. Shannon, <a href="/A331449/a331449.png">Image for n = 1</a>.
%H A331449 Scott R. Shannon, <a href="/A331449/a331449_1.png">Image for n = 2</a>.
%H A331449 Scott R. Shannon, <a href="/A331449/a331449_2.png">Image for n = 3</a>.
%H A331449 Scott R. Shannon, <a href="/A331449/a331449_3.png">Image for n = 4</a>.
%H A331449 Scott R. Shannon, <a href="/A331449/a331449_4.png">Image for n = 5</a>.
%H A331449 Scott R. Shannon, <a href="/A331449/a331449_5.png">Image for n = 10</a>.
%F A331449 By Euler's formula, a(n) = A331448(n) - A255011(n) + 1.
%Y A331449 Cf. A255011, A331448.
%Y A331449 For the circular analog see A006533, A007678, A007569, A135565.
%K A331449 nonn
%O A331449 0,2
%A A331449 _N. J. A. Sloane_, Jan 23 2020
%E A331449 a(11)-a(35) from _Giovanni Resta_, Jan 28 2020