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# OFFICIAL OEIS CONTRIBUTION TO EXISTING SEQUENCE A020727
# Edit/Contribute URL: https://oeis.org/edit?seq=A020727
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%C A020727 a(n) is the normalized determinant 2^(-n(n-1)/2) * det(D_n) of the (n+1) X (n+1) dyadic arithmetic diamond core matrix D_n(i,j) = 2^min(i,j) * (1 + delta_{i,j}) = gcd(2^i + 2^j, |2^i - 2^j|) for 0 <= i, j <= n. Equivalently, a(n) = 2^n * det(I_{n+1} + K_n(1/sqrt(2))), where K_n(rho) = [rho^|i-j|]_{0<=i,j<=n} is the Kac-Murdock-Szego Toeplitz matrix. - _Gareth Montgomery_, Oct 23 2026

%F A020727 a(n) = 2^(floor(n/2)) * A000129(n+2) for even n >= 0, and a(n) = 2^((n-1)/2) * A001333(n+2) for odd n >= 1. - _Gareth Montgomery_, Oct 23 2026
%F A020727 a(n) = 2^(-n*(n-1)/2) * det([gcd(2^i + 2^j, abs(2^i - 2^j))]_{0 <= i, j <= n}). - _Gareth Montgomery_, Oct 23 2026