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%I #28 Aug 11 2023 10:00:12
%S 0,0,1,0,1,0,1,1,1,0,2,1,1,1,2,1,2,0,2,2,2,0,3,2,1,2,3,1,3,0,3,3,2,1,
%T 4,2,1,2,4,2,4,0,2,4,3,1,5,3,2,2,4,2,3,2,4,5,2,0,6,2,3,3,5,3,4,2,2,5,
%U 4,0,7,3,2,4,5,4,4,0,5,6,4,1,6,4,2,4,6,2,6,2,4,5,2,3,8,6,2,3,6,2,7,0,5,8,4
%N Number of unordered solutions of x*y + y*z + z*x = n, x,y,z > 0.
%C a(n) is the number of distinct rectangular cuboids each one having integer surface area 2*n and integer edge lengths x, y and z. - _Felix Huber_, Aug 08 2023
%H T. D. Noe, <a href="/A066955/b066955.txt">Table of n, a(n) for n = 1..1000</a>
%F a(A094379(n)) = n and a(m) = n for m < A094379(n). - _Reinhard Zumkeller_, Mar 23 2012
%o (PARI) a(n)=sum(i=1,n,sum(j=1,i,sum(k=1,j,if(i*j+j*k+k*i-n,0,1))))
%o (Haskell)
%o a066955 n = length [(x,y,z) | x <- [1 .. a000196 (div n 3)],
%o y <- [x .. div n x],
%o z <- [y .. div (n - x*y) (x + y)],
%o x * y + (x + y) * z == n]
%o -- _Reinhard Zumkeller_, Mar 23 2012
%Y Cf. A000196, A066360, A094379.
%K nonn,easy
%O 1,11
%A _Colin Mallows_, Jan 26 2002
%E More terms from _Benoit Cloitre_, Feb 02 2003
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