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 A361635 #19 Apr 28 2023 16:23:19
%S A361635 0,1,3,4,7,16,17,28,70,85,125,392,379,704,3359,2248,4111,18510,14309,
%T A361635 30820
%N A361635 Number of strictly-convex unit-sided polygons with all internal angles equal to a multiple of Pi/n, ignoring rotational and reflectional copies.
%F A361635 a(p) = (2^(p-1)-1)/p + 2^((p-1)/2) for odd prime p. - _Andrew Howroyd_, Mar 22 2023
%e A361635 For n=3, a(3) is computed as follows: The base angle is Pi/3 (60 degrees). Thus any internal angle can only be either Pi/3 or 2*Pi/3. Call an interior angle with Pi/3 a "1" and with 2*Pi/3 a "2". Since all external angles will add to 2*Pi, we know that the only possible sequences (ignoring rotation and reflection) are {{1, 1, 1}, {1, 1, 2, 2}, {1, 2, 1, 2}, {1, 2, 2, 2, 2}, {2, 2, 2, 2, 2, 2}}. However, neither {1, 1, 2, 2} nor {1, 2, 2, 2, 2} forms a closed polygon. Thus the final set is {{1, 1, 1}, {1, 2, 1, 2}, {2, 2, 2, 2, 2, 2}}, which gives a(3) = 3.
%Y A361635 Cf. A164896, A361659.
%K A361635 nonn,more
%O A361635 1,3
%A A361635 _Roman Mecholsky_, Mar 18 2023
%E A361635 a(7) and a(9) corrected and a(11)-a(20) from _Andrew Howroyd_, Mar 22 2023