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A329504 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 at 45 degrees to grid lines.

%I A329504 #21 Nov 30 2019 10:42:01
%S A329504 1,1,2,1,4,2,1,4,5,2,1,4,8,4,2,1,4,8,8,4,2,1,4,8,12,6,4,2,1,4,8,12,11,
%T A329504 6,4,2,1,4,8,12,16,8,6,4,2,1,4,8,12,16,14,8,6,4,2,1,4,8,12,16,20,10,8,
%U A329504 6,4,2,1,4,8,12,16,20,17,10,8,6,4,2
%N A329504 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 at 45 degrees to grid lines.
%C A329504 By the "width" of the strip is meant the number of squares in a corner-to-corner ring around the cylinder.
%C A329504 For the case when the cuts are parallel to grid lines, see A329501.
%C A329504 See A329508 ... for coordination sequences for cylinders formed by rolling up the hexagonal grid ("carbon nanotubes").
%H A329504 N. J. A. Sloane, <a href="/A329504/a329504_1.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 A329504 <a href="/index/Con#coordination_sequences">Index entries for coordination sequences</a>
%F A329504 Let theta = (1+x)/(1-x). The g.f. for the coordination sequence for row n is theta*(1+2x+2x^2+...+2x^(n-1)-(n-1)*x^n).
%e A329504 Array begins:
%e A329504 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, ...
%e A329504 1, 4, 5, 4, 4, 4, 4, 4, 4, 4, 4, 4, ...
%e A329504 1, 4, 8, 8, 6, 6, 6, 6, 6, 6, 6, 6, ...
%e A329504 1, 4, 8, 12, 11, 8, 8, 8, 8, 8, 8, 8, ...
%e A329504 1, 4, 8, 12, 16, 14, 10, 10, 10, 10, 10, 10, ...
%e A329504 1, 4, 8, 12, 16, 20, 17, 12, 12, 12, 12, 12, ...
%e A329504 1, 4, 8, 12, 16, 20, 24, 20, 14, 14, 14, 14, ...
%e A329504 1, 4, 8, 12, 16, 20, 24, 28, 23, 16, 16, 16, ...
%e A329504 1, 4, 8, 12, 16, 20, 24, 28, 32, 26, 18, 18, ...
%e A329504 1, 4, 8, 12, 16, 20, 24, 28, 32, 36, 29, 20, ...
%e A329504 ...
%e A329504 The initial antidiagonals are:
%e A329504 1,
%e A329504 1,2,
%e A329504 1,4,2,
%e A329504 1,4,5,2,
%e A329504 1,4,8,4,2,
%e A329504 1,4,8,8,4,2,
%e A329504 1,4,8,12,6,4,2,
%e A329504 1,4,8,12,11,6,4,2,
%e A329504 1,4,8,12,16,8,6,4,2,
%e A329504 ...
%Y A329504 Rows 2,3,4 are A329505, A329506, A329507.
%Y A329504 Cf. A008574, A329501-A329517.
%K A329504 nonn,tabl,easy
%O A329504 1,3
%A A329504 _N. J. A. Sloane_, Nov 19 2019