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

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, 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, 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

Offset: 1

Author

Reinhard Zumkeller, Nov 24 2006

Keywords

• nonn

Comments

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

Links

• Reinhard Zumkeller, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A094178, A124934, A125217, A125218.

Cf. A193773.

Programs

Haskell

a125203 n = length [() | x <- [1 .. (n + 1) `div` 3],
                         let (y,m) = divMod (x + n) (4 * x - 1),
                         x <= y, m == 0]
-- Reinhard Zumkeller, Jan 02 2013

Mathematica

a[n_] := Solve[1<=x<=y && n == 4 x y - x - y, {x, y}, Integers] // Length;
Table[a[n], {n, 1, 105}] (* Jean-François Alcover, Oct 12 2021 *)