A212649 - OEIS

%I #28 Oct 27 2024 03:25:20

%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..n-1} sqrt(n^2 - k^2)).

%C Limit_{n->oo} a(n)/n^2 = Pi/4 = 0.78539816...

%F a(n) = floor(Sum_{k=0..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