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A175368 Number of integer 4-tuples (x,y,z,u) satisfying |x|^3+|y|^3+|z|^3+|u|^3 = n, -n <= x,y,z,u <= n. 1
1, 8, 24, 32, 16, 0, 0, 0, 8, 48, 96, 64, 0, 0, 0, 0, 24, 96, 96, 0, 0, 0, 0, 0, 32, 64, 0, 8, 48, 96, 64, 0, 16, 0, 0, 48, 192, 192, 0, 0, 0, 0, 0, 96, 192, 0, 0, 0, 0, 0, 0, 64, 0, 0, 24, 96, 96, 0, 0, 0, 0, 0, 96, 192, 8, 48, 96, 64, 0, 0, 96, 0, 48, 192, 192, 0, 0, 0, 0, 0, 96, 224, 64, 0 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

A variant of A000118 with cubes instead of squares.

LINKS

Table of n, a(n) for n=0..83.

FORMULA

Conjecture: g.f. ( 1+2*sum_{j>=1} x^(j^3) )^4.

EXAMPLE

a(1) = 8 counts (x,y,z,u) = (-1,0,0,0), (0,-1,0,0), (0,0,-1,0), (0,0,0,-1) and 4 more tuples with -1 replaced by +1.

a(2) = 24 counts (x,y,z,u) = (-1,-1,0,0), (-1,0,-1,0), (-1,0,0,-1), (-1,0,0,1) etc, all variants where two of the 4 values are zero and the other two +1 or -1.

CROSSREFS

Sequence in context: A038524 A261394 A162829 * A000118 A096727 A028660

Adjacent sequences:  A175365 A175366 A175367 * A175369 A175370 A175371

KEYWORD

nonn

AUTHOR

R. J. Mathar, Apr 24 2010

STATUS

approved

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Last modified March 23 22:30 EDT 2017. Contains 283985 sequences.