A372145 Number of domino tilings of the order n Aztec diamond which are centrally symmetric.
1, 2, 4, 12, 48, 288, 2304, 26880, 430080, 10035200, 321126400, 14836039680, 949506539520, 87734404251648, 11230003744210944, 2064716402685640704, 528567399087524020224, 194361783607326689722368, 99513233206951265137852416, 72958995691997968023051829248, 74710011588605919255605073149952
Offset: 0
Keywords
Links
- Bo-Yin Yang, Two Enumeration Problems about the Aztec Diamonds, MIT, 1991.
Formula
Let H_j(n) = Product_{1<=k
For n>=1, we have [see Bo-Yin Yang, Thm. 4.1]:
a(2*n) = 2^n * a(2*n-1);
a(4*n-1) = 2^(2*n^2-2*n+1)*H(4,4*n+3)*H(4,4*n-1)*(H(1,n)*H(1,n-1))^2/(H(2,2*n-1)*H(2,2*n+1))^3;
a(4*n+1) = 2^(2*n^2+1)*H(4,4*n+3)^2*H(1,n)^4/H(2,2*n+1)^6.