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Partial sums of A175375.
2

%I #5 May 01 2019 15:32:08

%S 1,7,19,27,27,27,27,27,27,27,27,27,27,27,27,27,33,57,81,81,81,81,81,

%T 81,81,81,81,81,81,81,81,81,93,117,117,117,117,117,117,117,117,117,

%U 117,117,117,117,117,117,125,125,125,125,125,125,125,125,125,125,125,125,125

%N Partial sums of A175375.

%C Number of integer triples (x,y,z) satisfying x^4+y^4+z^4 <= n, -n <= x,y,z <= n.

%H Robert Israel, <a href="/A175376/b175376.txt">Table of n, a(n) for n = 0..10000</a>

%F G.f.: (1 + 2*Sum_{j>0} x^(j^4))^3/(1-x). - _Robert Israel_, May 01 2019

%p N:= 100: # to get a(1)..a(N)

%p A:= Array(0..N):

%p for i from 0 while i^4 <= N do

%p if i=0 then ai:= 1 else ai:= 2 fi;

%p for j from 0 while i^4 + j^4 <= N do

%p if j=0 then aj:= 1 else aj:= 2 fi;

%p for k from 0 do

%p v:= i^4 + j^4 + k^4;

%p if v > N then break fi;

%p if k = 0 then ak:= 1 else ak:= 2 fi;

%p A[v]:= A[v] + ai*aj*ak;

%p od od od:

%p ListTools:-PartialSums(convert(A,list)); # _Robert Israel_, May 01 2019

%Y Cf. A117609, A175366, A175375.

%K nonn

%O 0,2

%A _R. J. Mathar_, Apr 24 2010