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A175362 Number of integer pairs (x,y) satisfying |x|^3 + |y|^3 = n, -n <= x,y <= n. 5
1, 4, 4, 0, 0, 0, 0, 0, 4, 8, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 8, 0, 0, 0, 0, 0, 0, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 8, 0, 0, 0, 0, 0, 0, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

Cube variant of A004018.

Obviously, a(n) must be 4*k, for k >= 0, n > 0. - Altug Alkan, Apr 09 2016

From Robert Israel, Jan 26 2017: (Start)

a(k^3*n) >= a(n) for k >= 1.

a(n) >= 16 for n in A001235.

a(A011541(n)) >= 8*n. (End)

LINKS

Robert Israel, Table of n, a(n) for n = 0..10000

FORMULA

G.f.: ( 1 + 2 * Sum_{j>=1} x^(j^3) )^2.

a(n^3) = 4 for n > 0. - Altug Alkan, Apr 09 2016

EXAMPLE

a(2) = 4 counts (x,y) = (-1,1), (1,1), (-1,-1) and (1,-1).

a(9) = 8 counts (x,y) = (-2,-1), (-2,1), (-1,-2), (-1,2), (1,-2), (1,2), (2,-1) and (2,1).

MAPLE

N:= 200: # to get a(0)..a(N)

G:= (1+2*add(x^(j^3), j=1..floor(N^(1/3))))^2:

seq(coeff(G, x, j), j=0..N); # Robert Israel, Jan 26 2017

CROSSREFS

Cf. A001235, A010057, A011541, A025446, A025455, A025464, A025468, A121980.

Sequence in context: A197243 A175372 A069191 * A189973 A282866 A098445

Adjacent sequences:  A175359 A175360 A175361 * A175363 A175364 A175365

KEYWORD

nonn

AUTHOR

R. J. Mathar, Apr 24 2010

EXTENSIONS

Invalid claim that belonged to A004018 removed by R. J. Mathar, Apr 24 2010

STATUS

approved

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Last modified May 7 05:10 EDT 2021. Contains 343636 sequences. (Running on oeis4.)