A175376 Partial sums of A175375.

1, 7, 19, 27, 27, 27, 27, 27, 27, 27, 27, 27, 27, 27, 27, 27, 33, 57, 81, 81, 81, 81, 81, 81, 81, 81, 81, 81, 81, 81, 81, 81, 93, 117, 117, 117, 117, 117, 117, 117, 117, 117, 117, 117, 117, 117, 117, 117, 125, 125, 125, 125, 125, 125, 125, 125, 125, 125, 125, 125, 125

Offset

0,2

Comments

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

Links

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

Formula

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

Maple

N:= 100: # to get a(1)..a(N)
A:= Array(0..N):
for i from 0 while i^4 <= N do
  if i=0 then ai:= 1 else ai:= 2 fi;
  for j from 0 while i^4 + j^4 <= N do
    if j=0 then aj:= 1 else aj:= 2 fi;
    for k from 0 do
      v:= i^4 + j^4 + k^4;
      if v > N then break fi;
      if k = 0 then ak:= 1 else ak:= 2 fi;
      A[v]:= A[v] + ai*aj*ak;
od od od:
ListTools:-PartialSums(convert(A, list)); # Robert Israel, May 01 2019

Crossrefs

Cf. A117609, A175366, A175375.

Sequence in context: A038593 A014439 A342160 * A175366 A117609 A122072

Adjacent sequences: A175373 A175374 A175375 * A175377 A175378 A175379

Keyword

nonn

Author

R. J. Mathar, Apr 24 2010

Status

approved