%I #22 Jan 30 2023 02:26:35
%S 16,96,192,896,960,4608,6720
%N Number of solutions to |dft(a)^2 + dft(b)^2 + dft(c)^2 + dft(d)^2| = 4n, where a,b,c,d are +1,-1 sequences of length n and dft(x) denotes the discrete Fourier transform of x.
%C Each solution (a,b,c,d) corresponds to a Hadamard matrix of quaternion type H = [[A, B, C, D], [-B, A, -D, C], [-C, D, A, -B], [-D, -C, B, A]], where A, B, C and D are circulant matrices formed by a, b, c and d, respectively.
%C 16 is a divisor of a(n), for all n. If (a,b,c,d) is a solution, then each of the 16 tuples ((+-)a, (+-)b, (+-)c, (+-)d) is also a solution.
%C a(n) >= A321338(n). Every solution (a,b,c,d) that is counted by A321338(n) is also counted by a(n).
%H Jeffery Kline, <a href="/A322639/a322639.txt">A complete list of solutions (a,b,c,d)</a>, for 1<=n<=7.
%H Jeffery Kline, <a href="/A322639/a322639_1.txt">List of tuples (a,b,c,d) to demonstrate that a(n)>0</a>, for 1<=n<=22 and n=24.
%Y Cf. A007299, A020985, A185064, A258218, A319594, A321338, A321851, A322617.
%K nonn,more
%O 1,1
%A _Jeffery Kline_, Dec 21 2018