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%I #24 Mar 19 2013 14:26:05
%S 1,3,8,13,21,30,41,53,67,82,99,118,138,159,183,207,234,262,291,322,
%T 355,389,425,462,501,542,584,628,673,720,768,818,870,923,977,1034,
%U 1091,1151,1212,1274,1338,1404,1471,1540,1610,1682,1756,1831,1908,1986,2066
%N a(n) = floor(sum_{k, 0 <= k <= n-1} sqrt(n^2 - k^2)).
%C a(n)/n^2 converges to pi/4 = 0.78539816... when n tends to infinity.
%F a(n) = Floor(sum_{k, 0<=k<=n-1} sqrt(A094728(n,k))).
%e A094728(4) is {16, 15, 12, 7). Hence, a(4) = floor(sqrt(16) + sqrt(15) + sqrt(12) + sqrt(7)) = floor(13.9828...) = 13.
%t Table[Floor[Sum[Sqrt[n^2 - k^2], {k, 0, n - 1}]], {n, 60}] (* _T. D. Noe_, Mar 19 2013 *)
%Y Cf. A003881, A094728.
%K nonn,easy
%O 1,2
%A _Philippe Deléham_, Mar 07 2013
%E a(16)-a(50) from _Giovanni Resta_, Mar 19 2013
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