A225987 - OEIS

%I #6 Oct 13 2021 06:08:12

%S 4,48,9,640,390,20,8960,20160,3192,60,129024,1106424,652784,48720,45,

%T 1892352,62606544,134432480,41801760,26010,420,28114944,3611217792,

%U 28244153600,36951200000,21594300,8168160,102,421724160,211096262400

%N T(n,k)=Number of pairs of orthogonal (-x,y) vectors of length k*(x+y), where x/y is the n-th rational <= 1, ordered first by y and then x, e.g. 1/1, 1/2, 1/3, 2/3, 1/4, 3/4 ...

%C Table starts

%C ..4....48......640........8960.........129024...........1892352

%C ..9...390....20160.....1106424.......62606544........3611217792

%C .20..3192...652784...134432480....28244153600.....6052498776192

%C .60.48720.41801760.36951200000.33792065269760.31520952625612800

%C .45.26010.21594300.15593341800.11432293516320..8690522384325600

%H R. H. Hardin, <a href="/A225987/b225987.txt">Table of n, a(n) for n = 1..1056</a>

%e Some solutions for n=1 k=4

%e .-1..1....1..1...-1.-1...-1.-1...-1..1....1..1...-1..1...-1.-1...-1.-1...-1..1

%e ..1..1...-1.-1...-1..1...-1..1....1..1...-1..1...-1.-1...-1..1...-1..1...-1.-1

%e .-1..1...-1..1....1..1...-1.-1...-1..1....1.-1....1.-1...-1.-1....1.-1....1.-1

%e .-1.-1...-1.-1....1.-1...-1.-1....1..1...-1.-1....1.-1...-1..1....1.-1....1.-1

%e ..1.-1....1.-1...-1.-1....1.-1...-1.-1...-1.-1....1..1...-1..1...-1..1...-1.-1

%e ..1.-1...-1..1....1..1....1..1...-1..1....1.-1....1.-1...-1.-1...-1.-1...-1.-1

%e ..1..1....1..1...-1..1....1.-1....1.-1....1.-1....1..1....1..1...-1.-1...-1.-1

%e ..1..1....1.-1...-1..1...-1..1...-1.-1...-1.-1....1..1....1.-1...-1.-1....1.-1

%Y Row 1 is A098402.

%K nonn,tabl

%O 1,1

%A _R. H. Hardin_, May 22 2013