A132104 Number of distinct Tsuro tiles which are square and have Q points per side.

1, 2, 30, 1447, 257107, 81898020, 39531524384, 26682303327353, 23987350539183237, 27705387002314059046, 39978873351170263411714, 70482753710219315731386411, 149071024096816130023228547735, 372528489217914304271725034290952, 1085920546070218942128273877774286532, 3651950796434146162433577686485443037885

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-A132105, A007769, A001147, A054499.

Programs

Maple

# B(n,m) gives the number of n-sided tiles with m points per side, allowing reflections (cf. comments in 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);
A132104 := m -> B(4,m);[seq(A132104(m),m=1..15)]; # Laurent Tournier, Jul 09 2014

Extensions

More terms from Laurent Tournier, Jul 09 2014