A033551 Closest integer to (Pi/4)*n^2.

1, 3, 7, 13, 20, 28, 38, 50, 64, 79, 95, 113, 133, 154, 177, 201, 227, 254, 284, 314, 346, 380, 415, 452, 491, 531, 573, 616, 661, 707, 755, 804, 855, 908, 962, 1018, 1075, 1134, 1195, 1257, 1320, 1385, 1452, 1521

Offset: 1

Author

Joe K. Crump (joecr(AT)carolina.rr.com)

Keywords

• easy
• nonn

Examples

			a(3)=7, since 3^2*Pi/4 = 7.06858347.
		

Links

• Harvey P. Dale, Table of n, a(n) for n = 1..1000

Crossrefs

Approximation for A051233.

Programs

GAP

List([1..50], n-> Int(Round(Atan(1.0)*n^2)) ); # G. C. Greubel, Oct 12 2019

Magma

R:= RealField(20); [Round(Pi(R)*n^2/4): n in [1..50]]; // G. C. Greubel, Oct 12 2019

Maple

seq(round((1/4)*Pi*n^2), n = 1..50); # G. C. Greubel, Oct 12 2019

Mathematica

Round[Pi/4 Range[50]^2] (* Harvey P. Dale, May 11 2016 *)

PARI

a(n) = round((Pi/4) * n^2); \\ Michel Marcus, Sep 02 2013

Sage

[round(pi*n^2/4) for n in (1..50)] # G. C. Greubel, Oct 12 2019

Formula

a(n) = round( (Pi/4) * n^2 ).