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A066955
Number of unordered solutions of x*y + y*z + z*x = n, x,y,z > 0.
8
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, 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, 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
OFFSET
1,11
COMMENTS
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
FORMULA
a(A094379(n)) = n and a(m) = n for m < A094379(n). - Reinhard Zumkeller, Mar 23 2012
PROG
(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))))
(Haskell)
a066955 n = length [(x, y, z) | x <- [1 .. a000196 (div n 3)],
y <- [x .. div n x],
z <- [y .. div (n - x*y) (x + y)],
x * y + (x + y) * z == n]
-- Reinhard Zumkeller, Mar 23 2012
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Colin Mallows, Jan 26 2002
EXTENSIONS
More terms from Benoit Cloitre, Feb 02 2003
STATUS
approved