

A224212


Number of nonnegative solutions to x^2 + y^2 <= n.


10



1, 3, 4, 4, 6, 8, 8, 8, 9, 11, 13, 13, 13, 15, 15, 15, 17, 19, 20, 20, 22, 22, 22, 22, 22, 26, 28, 28, 28, 30, 30, 30, 31, 31, 33, 33, 35, 37, 37, 37, 39, 41, 41, 41, 41, 43, 43, 43, 43, 45, 48, 48, 50, 52, 52, 52, 52, 52, 54, 54, 54, 56, 56, 56, 58, 62, 62, 62, 64
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OFFSET

0,2


LINKS

Seiichi Manyama, Table of n, a(n) for n = 0..1000


FORMULA

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


MATHEMATICA

nn = 68; t = Table[0, {nn}]; Do[d = x^2 + y^2; If[0 < d <= nn, t[[d]]++], {x, 0, nn}, {y, 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
k+=1
print(str(k), end=', ')


CROSSREFS

Cf. A000925 (first differences).
Cf. A000606 (number of nonnegative solutions to x^2 + y^2 + z^2 <= n).
Cf. A057655 (number of integer solutions to x^2 + y^2 <= n).
Sequence in context: A100478 A112376 A161359 * A078490 A282847 A047877
Adjacent sequences: A224209 A224210 A224211 * A224213 A224214 A224215


KEYWORD

nonn


AUTHOR

Alex Ratushnyak, Apr 01 2013


STATUS

approved



