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A132105 Number of distinct Tsuro tiles which are n-gonal in shape and have 2 points per side.

%I A132105 #6 Jul 09 2014 15:12:54
%S A132105 1,1,3,7,30,137,1065,10307,130040,1927853,32809979,625303343,
%T A132105 13178378742,304081128617,7623562484349,206343110670031,
%U A132105 5996839161108904,186254714746749377,6156752738537004317,215810382975655205399,7995774673152799224930
%N A132105 Number of distinct Tsuro tiles which are n-gonal in shape and have 2 points per side.
%C A132105 Turning over is allowed.
%C A132105 See A132100 for definition and comments.
%p A132105 # B(n,m) gives the number of n-sided tiles with m points per side, allowing reflections (cf. comments and formula of A132100)
%p A132105 with(numtheory): a:=(p,r)->piecewise(p mod 2 = 1,p^(r/2)*doublefactorial(r-1), sum(p^j*binomial(r, 2*j)*doublefactorial(2*j - 1), j = 0 .. floor(r/2)));
%p A132105 B := (n,m)->piecewise(n*m mod 2=1,0,add(phi(p)*a(p,m*n/p),p in divisors(n))/(2*n)+
%p A132105 piecewise(m mod 2=0, a(2,m*n/2)*2, a(2,m*n/2)+a(2,m*n/2-1))/4);
%p A132105 A132105 := n -> B(n,2);[seq(A132105(n),n=1..20)]; # _Laurent Tournier_, Jul 09 2014
%Y A132105 Cf. A132100-A132104, A007769, A001147, A054499.
%K A132105 nonn
%O A132105 0,3
%A A132105 _Keith F. Lynch_, Oct 31 2007
%E A132105 More terms from _Laurent Tournier_, Jul 09 2014