OFFSET
0,2
LINKS
Bo-Yin Yang, Two Enumeration Problems about the Aztec Diamonds, MIT, 1991.
FORMULA
Let H_j(n) = Product_{1<=k<n/j} (n-j*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.
CROSSREFS
KEYWORD
nonn
AUTHOR
Ludovic Schwob, Jun 27 2024
STATUS
approved