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A132102 Number of distinct Tsuro tiles which are n-gonal in shape and have 2 points per side.

%I A132102 #19 Jan 26 2020 18:20:33
%S A132102 1,1,3,7,35,193,1799,19311,254143,3828921,65486307,1249937335,
%T A132102 26353147811,608142583137,15247011443103,412685556939751,
%U A132102 11993674252049647,372509404162520641,12313505313357313047,431620764875678503143,15991549339008732109899
%N A132102 Number of distinct Tsuro tiles which are n-gonal in shape and have 2 points per side.
%C A132102 Turning over is not allowed.
%C A132102 See A132100 for definition and comments.
%C A132102 Even and odd terms can be computed with the help of Burnside Lemma and recursive sequences. - _Lionel RAVEL_, Sep 18 2013
%H A132102 Andrew Howroyd, <a href="/A132102/b132102.txt">Table of n, a(n) for n = 0..200</a>
%F A132102 a(n) = (1/n)*Sum_{d|n} phi(d)*alpha(d, n/d), where phi = Euler's totient function,
%F A132102 alpha(p,q) = Sum_{j=0..q} p^j * binomial(2q, 2j) * (2j-1)!! if p even,
%F A132102 = p^q * (2q-1)!! if p odd. (cf. also A132100) - _Laurent Tournier_, Jul 09 2014
%p A132102 with(numtheory): a:=(p,q)->piecewise(p mod 2 = 1, p^q*doublefactorial(2*q - 1), sum(p^j*binomial(2*q, 2*j)*doublefactorial(2*j - 1), j = 0 .. q));
%p A132102 A132102 := n->add(phi(p)*a(p,n/p),p in divisors(n))/n;
%p A132102 [seq(A132102(n),n=1..20)]; # _Laurent Tournier_, Jul 09 2014
%o A132102 (PARI) a(n)={if(n<1, n==0, sumdiv(n, d, my(m=n/d); eulerphi(d)*sum(j=0, m, (d%2==0 || m-j==0) * binomial(2*m, 2*j) * d^j * (2*j)! / (j!*2^j) ))/n)} \\ _Andrew Howroyd_, Jan 26 2020
%Y A132102 Cf. A001147, A007769, A054499, A132100, A132101, A132103, A132104, A132105.
%K A132102 nonn
%O A132102 0,3
%A A132102 _Keith F. Lynch_, Oct 31 2007
%E A132102 More terms from _Lionel RAVEL_, Sep 18 2013
%E A132102 a(9) and a(10) corrected, and addition of more terms using formula given above by _Laurent Tournier_, Jul 09 2014