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A156790
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Number of first quadrant lattice squares inside the circle x^2+y^2=(2^n)^2
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1
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0, 1, 8, 41, 183, 770, 3149, 12730, 51209, 205356, 822500, 3292134, 13172634, 52698912, 210812207, 843281848, 3373193506, 13492906143, 53971888157, 15888078393, 863553363881, 3454215553470, 13816866413106, 55267474046659
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OFFSET
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0,3
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COMMENTS
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a(n)/4^n converges to Pi/4 from below.
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LINKS
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EXAMPLE
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Let + represent a square inside the circle and x a square traversed by the circle.
xx
+x a(1)=1
xxx
++xx
+++x
+++x a(2)=8
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PROG
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(PARI) a(n)=sum(m=1, 2^n-1, floor(sqrt(4^n-m^2)))
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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