This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A329501 #46 May 29 2022 21:34:19
%S A329501 1,1,2,1,3,2,1,4,4,2,1,4,6,4,2,1,4,7,6,4,2,1,4,8,8,6,4,2,1,4,8,10,8,6,
%T A329501 4,2,1,4,8,11,10,8,6,4,2,1,4,8,12,12,10,8,6,4,2,1,4,8,12,14,12,10,8,6,
%U A329501 4,2
%N A329501 Array read by upward antidiagonals: row n = coordination sequence for cylinder formed by rolling up a strip of width n squares cut from the square grid by cuts parallel to grid lines.
%C A329501 For the case when the cuts are at 45 degrees to the grid lines, see A329504.
%C A329501 See A329508, A329512, and A329515 for coordination sequences for cylinders formed by rolling up the hexagonal grid ("carbon nanotubes").
%C A329501 The g.f.s for the rows can easily be found using the "trunks and branches" method (see Goodman-Strauss and Sloane). In the illustration for n=5, there are two trunks (blue) and ten branches (red).
%H A329501 Chaim Goodman-Strauss and N. J. A. Sloane, <a href="https://doi.org/10.1107/S2053273318014481">A Coloring Book Approach to Finding Coordination Sequences</a>, Acta Cryst. A75 (2019), 121-134, also <a href="http://NeilSloane.com/doc/Cairo_final.pdf">on NJAS's home page</a>. Also <a href="http://arxiv.org/abs/1803.08530">arXiv:1803.08530</a>.
%H A329501 N. J. A. Sloane, <a href="/A329501/a329501.pdf">Illustration for rows 1 through 5</a>, showing vertices of cylinder labeled with distance from base point (c = n is the width (or circumference)). The cylinders are formed by identifying the black lines.
%H A329501 <a href="/index/Con#coordination_sequences">Index entries for coordination sequences</a>
%F A329501 Let theta = (1+x)/(1-x).
%F A329501 If n = 2*k, the g.f. for the coordination sequence for row n is theta*(1+2*x+2*x^2+...+2*x^(k-1)+x^k).
%F A329501 If n = 2*k+1, the g.f. for the coordination sequence for row n is theta*(1+2*x+2*x^2+...+2*x^k).
%e A329501 Array begins:
%e A329501 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, ...
%e A329501 1, 3, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, ...
%e A329501 1, 4, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, ...
%e A329501 1, 4, 7, 8, 8, 8, 8, 8, 8, 8, 8, 8, ...
%e A329501 1, 4, 8, 10, 10, 10, 10, 10, 10, 10, 10, 10, ...
%e A329501 1, 4, 8, 11, 12, 12, 12, 12, 12, 12, 12, 12, ...
%e A329501 1, 4, 8, 12, 14, 14, 14, 14, 14, 14, 14, 14, ...
%e A329501 1, 4, 8, 12, 15, 16, 16, 16, 16, 16, 16, 16, ...
%e A329501 1, 4, 8, 12, 16, 18, 18, 18, 18, 18, 18, 18, ...
%e A329501 1, 4, 8, 12, 16, 19, 20, 20, 20, 20, 20, 20, ...
%e A329501 ...
%e A329501 The initial antidiagonals are:
%e A329501 1;
%e A329501 1, 2;
%e A329501 1, 3, 2;
%e A329501 1, 4, 4, 2;
%e A329501 1, 4, 6, 4, 2;
%e A329501 1, 4, 7, 6, 4, 2;
%e A329501 1, 4, 8, 8, 6, 4, 2;
%e A329501 1, 4, 8, 10, 8, 6, 4, 2;
%e A329501 1, 4, 8, 11, 10, 8, 6, 4, 2;
%e A329501 1, 4, 8, 12, 12, 10, 8, 6, 4, 2;
%e A329501 1, 4, 8, 12, 14, 12, 10, 8, 6, 4, 2;
%e A329501 ...
%Y A329501 Rows 1,2,3,4,5 are A040000, A113311, A329502, A115291, A329503.
%Y A329501 Cf. A008574, A329504-A329517.
%K A329501 nonn,tabl,easy
%O A329501 1,3
%A A329501 _N. J. A. Sloane_, Nov 19 2019