Search: id:A014198
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%I A014198
%S A014198 0,4,8,8,12,20,20,20,24,28,36,36,36,44,44,44,48,56,60,60,68,68,68,68,
%T A014198 68,80,88,88,88,96,96,96,100,100,108,108,112,120,120,120,128,136,136,
%U A014198 136,136,144,144,144,144,148,160,160,168,176,176,176,176,176,184,184
%N A014198 Number of integer solutions to x^2+y^2 <= n excluding (0,0).
%C A014198 a(32)/32 = 100/32 = 3.125; lim a(n)/n = Pi.
%D A014198 G. H. Hardy and E. M. Wright, An Introduction to the Theory of Numbers, 
               5th ed., Oxford Univ. Press, 1979, th. 339
%H A014198 Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/
               SumofSquaresFunction.html">Link to a section of The World of Mathematics.</
               a>
%e A014198 For n=2 the 8 solutions are (x,y) = (+-1,0), (0,+-1), (+-1,+-1).
%p A014198 with(numtheory): for n from 0 to 60 do h[ n ] := nops([ thue( abs( x^2+y^2) 
               <= n, [ x,y ] ) ]); od; [ seq(h[ i ],i=0..60) ];
%o A014198 (PARI) a(n)=local(j); j=sqrtint(n); sum(x=-j,j,sum(y=-j,j,x^2+y^2<=n))-1
%Y A014198 Cf. A014200. 4 * partial sums of A002654 = -1 + partial sums of A004018.
%Y A014198 Sequence in context: A072541 A141719 A098352 this_sequence A159786 A083744 
               A114027
%Y A014198 Adjacent sequences: A014195 A014196 A014197 this_sequence A014199 A014200 
               A014201
%K A014198 nonn,easy
%O A014198 0,2
%A A014198 N. J. A. Sloane (njas(AT)research.att.com).

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