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 A001182 Number of cells of square lattice of edge 1/n inside quadrant of unit circle centered at 0. 11

%I

%S 0,1,4,8,15,22,30,41,54,69,83,98,119,139,162,183,208,234,263,294,322,

%T 357,390,424,465,504,545,585,628,675,719,770,819,872,928,977,1036,

%U 1090,1155,1216,1274,1339,1404,1475,1545,1610,1683,1755,1832,1911,1992,2072

%N Number of cells of square lattice of edge 1/n inside quadrant of unit circle centered at 0.

%H Michael De Vlieger, <a href="/A001182/b001182.txt">Table of n, a(n) for n = 1..10000</a>

%F a(n) = Sum_{k=1..n-1} floor(sqrt(n^2-k^2)). - Horst Kraemer (horst.kraemer(AT)epost.de) Apr 07 2004

%F a(n) = A261849(2*n)/4 = (A281795(n)-A242118(n))/4. - _Andrey Zabolotskiy_, Jan 30 2017

%F 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

%t Table[Sum[Floor@ Sqrt[n^2 - k^2], {k, n - 1}], {n, 52}] (* _Michael De Vlieger_, Jan 30 2017 *)

%Y Cf. A261849, A242118, A281795.

%K nonn

%O 1,3

%A Tihamer von Ghyczy (ghyczy(AT)esinet.net)

%E More terms from Klaus Strassburger (strass(AT)ddfi.uni-duesseldorf.de), Jan 19 2000

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Last modified June 1 09:53 EDT 2020. Contains 334762 sequences. (Running on oeis4.)