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

1, 1, 3, 7, 30, 137, 1065, 10307, 130040, 1927853, 32809979, 625303343, 13178378742, 304081128617, 7623562484349, 206343110670031, 5996839161108904, 186254714746749377, 6156752738537004317, 215810382975655205399, 7995774673152799224930

Offset: 0

Author

Keith F. Lynch, Oct 31 2007

Keywords

• nonn

Comments

Turning over is allowed.

See A132100 for definition and comments.

Crossrefs

Cf. A132100-A132104, A007769, A001147, A054499.

Programs

Maple

# B(n,m) gives the number of n-sided tiles with m points per side, allowing reflections (cf. comments and formula of A132100)
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)));
B := (n,m)->piecewise(n*m mod 2=1,0,add(phi(p)*a(p,m*n/p),p in divisors(n))/(2*n)+
piecewise(m mod 2=0, a(2,m*n/2)*2, a(2,m*n/2)+a(2,m*n/2-1))/4);
A132105 := n -> B(n,2);[seq(A132105(n),n=1..20)]; # Laurent Tournier, Jul 09 2014

Extensions

More terms from Laurent Tournier, Jul 09 2014