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

0,2

Links

Table of n, a(n) for n=0..20.

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

Cf. A006125, A005158.

Sequence in context: A030801 A263867 A326863 * A082480 A093934 A109458

Adjacent sequences: A372142 A372143 A372144 * A372146 A372147 A372148

Keyword

nonn

Author

Ludovic Schwob, Jun 27 2024

Status

approved