OFFSET
3,2
COMMENTS
LINKS
Andrew Howroyd, Table of n, a(n) for n = 3..1000
FORMULA
EXAMPLE
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:
d = 1: {2}
d = 2: {04, 13}
d = 3: {015, 024, 033, 042, 051, 114, 123, 132}
In total there are 11 possibilities, so a(6) = 11.
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.
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.
PROG
(PARI) a(n) = -(1+(-1)^n)/2 + (1/n)*sumdiv(n, d, (eulerphi(n/d)-moebius(n/d)) * binomial(3*d-1, d-1));
CROSSREFS
KEYWORD
nonn
AUTHOR
Andrew Howroyd, Sep 14 2017
STATUS
approved