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 A224213 Number of nonnegative solutions to x^2 + y^2 + z^2 + u^2 <= n. 8
 1, 5, 11, 15, 20, 32, 44, 48, 54, 70, 88, 100, 108, 124, 148, 160, 165, 189, 219, 235, 253, 281, 305, 317, 329, 357, 399, 427, 439, 475, 523, 539, 545, 581, 623, 659, 688, 716, 764, 792, 810, 858, 918, 946, 970, 1030, 1078, 1102, 1110, 1154, 1226, 1274, 1304, 1352 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 LINKS FORMULA G.f.: (1/(1 - x))*(Sum_{k>=0} x^(k^2))^4. - Ilya Gutkovskiy, Mar 14 2017 MATHEMATICA nn = 50; t = Table[0, {nn}]; Do[d = x^2 + y^2 + z^2 + u^2; If[0 < d <= nn, t[[d]]++], {x, 0, nn}, {y, 0, nn}, {z, 0, nn}, {u, 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 for u in range(99): su = sz + u*u if su>n: break k+=1 print(str(k), end=', ') CROSSREFS Cf. A014110 (first differences). Cf. A224212 (number of nonnegative solutions to x^2 + y^2 <= n). Cf. A000606 (number of nonnegative solutions to x^2 + y^2 + z^2 <= n). Cf. A046895 (number of integer solutions to x^2 + y^2 + z^2 + u^2 <= n). Sequence in context: A314035 A314036 A314037 * A036787 A182664 A299976 Adjacent sequences: A224210 A224211 A224212 * A224214 A224215 A224216 KEYWORD nonn AUTHOR Alex Ratushnyak, Apr 01 2013 STATUS approved

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Last modified March 31 17:28 EDT 2023. Contains 361668 sequences. (Running on oeis4.)