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A224213
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Number of nonnegative solutions to x^2 + y^2 + z^2 + u^2 <= n.
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8
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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)
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OFFSET
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0,2
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LINKS
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Table of n, a(n) for n=0..53.
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FORMULA
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G.f.: (1/(1 - x))*(Sum_{k>=0} x^(k^2))^4. - Ilya Gutkovskiy, Mar 14 2017
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MATHEMATICA
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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 *)
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PROG
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(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=', ')
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CROSSREFS
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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
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KEYWORD
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nonn
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AUTHOR
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Alex Ratushnyak, Apr 01 2013
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STATUS
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approved
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