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 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 (list; graph; refs; listen; history; text; internal format)
 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

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Last modified March 28 23:19 EDT 2023. Contains 361596 sequences. (Running on oeis4.)