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%I #13 Nov 11 2018 00:43:00
%S 1,2,1,11,1,42,10,202,1,1077,1,5539,210,30666,1,174620,1,1001642,5547,
%T 5864751,1,34799997,201,208267321,173593,1258579693,1,7664723137,1,
%U 46976034378,5864759,289628805624,5738,1794967236906,1,11175157356523,208267329
%N Number of distinct convex equilateral n-gons having rotational symmetry and with corner angles of m*Pi/n (0 < m <= n).
%C Subset of polygons of A262181 having rotational symmetry. Polygons that differ only by rotation are not considered as distinct. See A262181 for illustrations of initial terms. The first difference between this sequence and A262181 is at a(9).
%H Andrew Howroyd, <a href="/A292355/b292355.txt">Table of n, a(n) for n = 3..1000</a>
%F a(n) = -(1+(-1)^n)/2 + (1/n)*Sum_{d | n} (phi(n/d)-moebius(n/d)) * binomial(3*d-1, d-1).
%F a(n) = A262181(n) for n prime or twice prime.
%F Conjecture: a(2^n) = A262181(2^n).
%e Case n=6: The ways to select d angles that are multiples of Pi/n and sum to 2*d which are nonequivalent up to rotation and d is a proper factor of 6 are:
%e d = 1: {2}
%e d = 2: {04, 13}
%e d = 3: {015, 024, 033, 042, 051, 114, 123, 132}
%e In total there are 11 possibilities, so a(6) = 11.
%e In the above, 22 and 222 are excluded from the possibilities for d = 2 and 3 because they correspond to the regular hexagon that is covered by d = 1.
%e Also, 006 has been excluded from d = 3 since 6 corresponds to an angle of 180 degrees which is disallowed by this sequence. This would be the flattened polygon of three sides in one direction and then three back in the opposite.
%o (PARI) a(n) = -(1+(-1)^n)/2 + (1/n)*sumdiv(n,d, (eulerphi(n/d)-moebius(n/d)) * binomial(3*d-1, d-1));
%Y Cf. A262181.
%K nonn
%O 3,2
%A _Andrew Howroyd_, Sep 14 2017
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