[seqfan] Re: Number of solutions of a*b + c*d + ... + y*z = 0 (mod n)

[Max Alekseyev]

On Sun, Sep 5, 2010 at 9:10 PM, Ron Hardin <rhhardin at att.net> wrote:

> 0,0,0,1,0,2,0,3,3,4,0,9,0,6,8,10,0,15,0,17,12,10,0,27,10,12,15,25,0,38,
> 0,26,20,16,24,51,0,18,24,51,0,56,0,41,51,22,0,74,21,50,32,49,0,69,40,75,
> 36,28,0,121,0,30,75,68,48,92,0,65,44,106,0,141,0,36,90,73,60,110,0,138
> Number of distinct no-zero solutions of sum{i=1..1}(x(2i-1)*x(2i)) = 0 (mod n)
> <a href="b000001.txt">Table of n, a(n) for n=1..152</a>

The formula for this one is

a(n) = A174088(n) - n = ( A018804(n) + A000188(n) )/2 - n

Max