A175377 a(n) = A175376(n^2).

1, 7, 27, 27, 33, 81, 117, 125, 125, 131, 251, 275, 275, 311, 335, 335, 349, 493, 493, 613, 613, 637, 637, 697, 697, 727, 871, 991, 999, 1023, 1143, 1143, 1191, 1191, 1215, 1215, 1281, 1449, 1569, 1617, 1737, 1785, 1785, 1809, 1889, 1985, 1985, 2033, 2033

Offset

0,2

Comments

Number of integer triples (x,y,z) satisfying x^4+y^4+z^4 <= n^2, -n <= x,y,z <= n.

Links

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

Maple

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

Crossrefs

Cf. A055410, A175370.

Sequence in context: A342930 A166406 A243006 * A323113 A205861 A215446

Adjacent sequences: A175374 A175375 A175376 * A175378 A175379 A175380

Keyword

nonn

Author

R. J. Mathar, Apr 24 2010

Status

approved