A212649 a(n) = floor(Sum_{k=0..n-1} sqrt(n^2 - k^2)).

1, 3, 8, 13, 21, 30, 41, 53, 67, 82, 99, 118, 138, 159, 183, 207, 234, 262, 291, 322, 355, 389, 425, 462, 501, 542, 584, 628, 673, 720, 768, 818, 870, 923, 977, 1034, 1091, 1151, 1212, 1274, 1338, 1404, 1471, 1540, 1610, 1682, 1756, 1831, 1908, 1986, 2066

Offset

1,2

Comments

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

Links

Table of n, a(n) for n=1..51.

Formula

a(n) = floor(Sum_{k=0..n-1} sqrt(A094728(n,k))).

Example

A094728(4) is (16, 15, 12, 7). Hence, a(4) = floor(sqrt(16) + sqrt(15) + sqrt(12) + sqrt(7)) = floor(13.9828...) = 13.

Mathematica

Table[Floor[Sum[Sqrt[n^2 - k^2], {k, 0, n - 1}]], {n, 60}] (* T. D. Noe, Mar 19 2013 *)

Crossrefs

Cf. A003881, A094728.

Sequence in context: A317194 A319128 A094110 * A084535 A351355 A194427

Adjacent sequences: A212646 A212647 A212648 * A212650 A212651 A212652

Keyword

nonn,easy

Author

Philippe Deléham, Mar 07 2013

Extensions

a(16)-a(50) from Giovanni Resta, Mar 19 2013

Status

approved