A000606 Number of nonnegative solutions to x^2 + y^2 + z^2 <= n. (Formerly M3294 N1329)

1, 4, 7, 8, 11, 17, 20, 20, 23, 29, 35, 38, 39, 45, 51, 51, 54, 63, 69, 72, 78, 84, 87, 87, 90, 99, 111, 115, 115, 127, 133, 133, 136, 142, 151, 157, 163, 169, 178, 178, 184, 199, 205, 208, 211, 223, 229, 229, 230, 239, 254, 260, 266, 278, 290, 290, 296

Offset

0,2

References

H. Gupta, A Table of Values of N_3(t), Proc. National Institute of Sciences of India, 13 (1947), 35-63.

N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).

N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

Links

T. D. Noe, Table of n, a(n) for n = 0..1000

Formula

G.f.: (1/(1 - x))*(Sum_{k>=0} x^(k^2))^3. - Ilya Gutkovskiy, Mar 14 2017

Mathematica

nn = 50; t = Table[0, {nn}]; Do[d = x^2 + y^2 + z^2; If[0 < d <= nn, t[[d]]++], {x, 0, nn}, {y, 0, nn}, {z, 0, nn}]; Accumulate[Join[{1}, t]] (* T. D. Noe, Apr 01 2013 *)

Prog

(Python)
for n in range(99):
  k = 0
  for x in range(99):
    s = x*x
    if s > n: break
    for y in range(99):
        sy = s + y*y
        if sy > n: break
        for z in range(99):
            sz = sy + z*z
            if sz > n: break
            k += 1
  print(str(k), end=', ')
# Alex Ratushnyak, Apr 01 2013

Crossrefs

Cf. A000604, A117609.

Cf. A002102 (first differences).

Sequence in context: A024621 A375572 A296029 * A215458 A061932 A270336

Adjacent sequences: A000603 A000604 A000605 * A000607 A000608 A000609

Keyword

nonn

Author

N. J. A. Sloane

Extensions

More terms from Sean A. Irvine, Dec 01 2010

Status

approved