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A081757 Number of ways to write n as i*j+i-j, 0<i<j. 4

%I #9 May 24 2013 21:29:07

%S 0,0,0,0,1,1,1,1,1,1,2,1,2,1,2,1,2,1,3,1,2,2,2,1,3,1,2,2,3,1,3,1,3,2,

%T 2,1,4,1,2,2,4,1,3,1,3,3,2,1,4,1,3,2,3,1,4,2,3,2,2,1,6,1,2,2,3,2,4,1,

%U 3,2,4,1,5,1,2,3,3,2,4,1,4,2,2,1,6,2,2,2,4,1,5,2,3,2,2,2,6,1,3,2,4,1,4,1,4

%N Number of ways to write n as i*j+i-j, 0<i<j.

%H Reinhard Zumkeller, <a href="/A081757/b081757.txt">Table of n, a(n) for n = 1..1000</a>

%F G.f.: Sum(x^(n^2+3*n)/(1-x^n),n = 1 .. infinity). - _Vladeta Jovovic_, May 13 2008

%e n=25 = 2*23+2-23 = 3*11+3-11 = 4*7+4-7, therefore a(25)=3.

%o (Haskell)

%o a081757 n = length [() | j <- [2..n], i <- [1..j-1], i * j + i - j == n]

%o -- _Reinhard Zumkeller_, May 24 2013

%Y Cf. A072670.

%K nonn

%O 1,11

%A _Reinhard Zumkeller_, Apr 08 2003

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