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 A001182 Number of cells of square lattice of edge 1/n inside quadrant of unit circle centered at 0. 11
 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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,3 LINKS Michael De Vlieger, Table of n, a(n) for n = 1..10000 FORMULA 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 MATHEMATICA Table[Sum[Floor@ Sqrt[n^2 - k^2], {k, n - 1}], {n, 52}] (* Michael De Vlieger, Jan 30 2017 *) CROSSREFS Cf. A261849, A242118, A281795. Sequence in context: A024916 A212539 A102216 * A264599 A122247 A126255 Adjacent sequences:  A001179 A001180 A001181 * A001183 A001184 A001185 KEYWORD nonn AUTHOR Tihamer von Ghyczy (ghyczy(AT)esinet.net) EXTENSIONS More terms from Klaus Strassburger (strass(AT)ddfi.uni-duesseldorf.de), Jan 19 2000 STATUS approved

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Last modified April 7 19:49 EDT 2020. Contains 333306 sequences. (Running on oeis4.)