A125203 - OEIS

%I #14 Oct 12 2021 21:57:54

%S 0,1,0,0,1,0,0,1,0,0,1,1,0,1,0,0,1,0,1,1,0,0,1,0,0,2,0,0,1,1,0,1,1,0,

%T 1,0,0,1,0,1,2,0,0,1,0,0,2,0,0,1,0,1,1,1,0,2,0,0,1,0,1,1,1,0,1,0,0,2,

%U 0,0,2,0,0,2,1,0,1,0,0,1,0,1,1,0,1,2,0,0,2,1,0,1,0,0,1,2,0,1,0,0,2,0,1,1,0

%N Number of ways to write n as 4*x*y - x - y with 1<=x<=y.

%C a(A094178(n))=0; a(A124934(n))>0; a(A125217(n))=1; a(A125218(n))>1.

%H Reinhard Zumkeller, <a href="/A125203/b125203.txt">Table of n, a(n) for n = 1..10000</a>

%t a[n_] := Solve[1<=x<=y && n == 4 x y - x - y, {x, y}, Integers] // Length;

%t Table[a[n], {n, 1, 105}] (* _Jean-François Alcover_, Oct 12 2021 *)

%o (Haskell)

%o a125203 n = length [() | x <- [1 .. (n + 1) `div` 3],

%o                          let (y,m) = divMod (x + n) (4 * x - 1),

%o                          x <= y, m == 0]

%o -- _Reinhard Zumkeller_, Jan 02 2013

%Y Cf. A094178, A124934, A125217, A125218.

%Y Cf. A193773.

%K nonn

%O 1,26

%A _Reinhard Zumkeller_, Nov 24 2006