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Search: id:A014198
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| A014198 |
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Number of integer solutions to x^2+y^2 <= n excluding (0,0). |
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+0
5
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| 0, 4, 8, 8, 12, 20, 20, 20, 24, 28, 36, 36, 36, 44, 44, 44, 48, 56, 60, 60, 68, 68, 68, 68, 68, 80, 88, 88, 88, 96, 96, 96, 100, 100, 108, 108, 112, 120, 120, 120, 128, 136, 136, 136, 136, 144, 144, 144, 144, 148, 160, 160, 168, 176, 176, 176, 176, 176, 184, 184
(list; graph; listen)
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OFFSET
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0,2
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COMMENT
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a(32)/32 = 100/32 = 3.125; lim a(n)/n = Pi.
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REFERENCES
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G. H. Hardy and E. M. Wright, An Introduction to the Theory of Numbers, 5th ed., Oxford Univ. Press, 1979, th. 339
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LINKS
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Eric Weisstein's World of Mathematics, Link to a section of The World of Mathematics.
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EXAMPLE
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For n=2 the 8 solutions are (x,y) = (+-1,0), (0,+-1), (+-1,+-1).
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MAPLE
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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) ];
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PROGRAM
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(PARI) a(n)=local(j); j=sqrtint(n); sum(x=-j, j, sum(y=-j, j, x^2+y^2<=n))-1
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CROSSREFS
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Cf. A014200. 4 * partial sums of A002654 = -1 + partial sums of A004018.
Sequence in context: A072541 A141719 A098352 this_sequence A159786 A083744 A114027
Adjacent sequences: A014195 A014196 A014197 this_sequence A014199 A014200 A014201
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KEYWORD
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nonn,easy
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AUTHOR
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N. J. A. Sloane (njas(AT)research.att.com).
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