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A125203 Number of ways to write n as 4*x*y - x - y with 1<=x<=y.

%I A125203 #14 Oct 12 2021 21:57:54
%S A125203 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 A125203 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 A125203 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 A125203 Number of ways to write n as 4*x*y - x - y with 1<=x<=y.
%C A125203 a(A094178(n))=0; a(A124934(n))>0; a(A125217(n))=1; a(A125218(n))>1.
%H A125203 Reinhard Zumkeller, <a href="/A125203/b125203.txt">Table of n, a(n) for n = 1..10000</a>
%t A125203 a[n_] := Solve[1<=x<=y && n == 4 x y - x - y, {x, y}, Integers] // Length;
%t A125203 Table[a[n], {n, 1, 105}] (* _Jean-François Alcover_, Oct 12 2021 *)
%o A125203 (Haskell)
%o A125203 a125203 n = length [() | x <- [1 .. (n + 1) `div` 3],
%o A125203                          let (y,m) = divMod (x + n) (4 * x - 1),
%o A125203                          x <= y, m == 0]
%o A125203 -- _Reinhard Zumkeller_, Jan 02 2013
%Y A125203 Cf. A094178, A124934, A125217, A125218.
%Y A125203 Cf. A193773.
%K A125203 nonn
%O A125203 1,26
%A A125203 _Reinhard Zumkeller_, Nov 24 2006