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A001182
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Number of cells of square lattice of edge 1/n inside quadrant of unit circle centered at 0.
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19
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0, 1, 4, 8, 15, 22, 30, 41, 54, 69, 83, 98, 119, 139, 162, 183, 208, 234, 263, 294, 322, 357, 390, 424, 465, 504, 545, 585, 628, 675, 719, 770, 819, 872, 928, 977, 1036, 1090, 1155, 1216, 1274, 1339, 1404, 1475, 1545, 1610, 1683, 1755, 1832, 1911, 1992, 2072
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OFFSET
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1,3
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LINKS
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Michael De Vlieger, Table of n, a(n) for n = 1..10000
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FORMULA
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a(n) = Sum_{k=1..n-1} floor(sqrt(n^2-k^2)). - Horst Kraemer (horst.kraemer(AT)epost.de) Apr 07 2004
a(n) = A261849(2*n)/4 = (A281795(n)-A242118(n))/4. - Andrey Zabolotskiy, Jan 30 2017
a(n) = [x^(n^2)] (theta_3(x) - 1)^2/(4*(1 - x)), where theta_3() is the Jacobi theta function. - Ilya Gutkovskiy, Apr 17 2018
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MATHEMATICA
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Table[Sum[Floor@ Sqrt[n^2 - k^2], {k, n - 1}], {n, 52}] (* Michael De Vlieger, Jan 30 2017 *)
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CROSSREFS
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Cf. A261849, A242118, A281795.
Sequence in context: A024916 A212539 A102216 * A264599 A122247 A126255
Adjacent sequences: A001179 A001180 A001181 * A001183 A001184 A001185
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KEYWORD
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nonn
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AUTHOR
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Tihamer von Ghyczy (ghyczy(AT)esinet.net)
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EXTENSIONS
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More terms from Klaus Strassburger (strass(AT)ddfi.uni-duesseldorf.de), Jan 19 2000
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STATUS
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approved
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