login

Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).

Closest integer to (Pi/4)*n^2.
1

%I #12 Sep 08 2022 08:44:51

%S 1,3,7,13,20,28,38,50,64,79,95,113,133,154,177,201,227,254,284,314,

%T 346,380,415,452,491,531,573,616,661,707,755,804,855,908,962,1018,

%U 1075,1134,1195,1257,1320,1385,1452,1521

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

%H Harvey P. Dale, <a href="/A033551/b033551.txt">Table of n, a(n) for n = 1..1000</a>

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

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

%p seq(round((1/4)*Pi*n^2), n = 1..50); # _G. C. Greubel_, Oct 12 2019

%t Round[Pi/4 Range[50]^2] (* _Harvey P. Dale_, May 11 2016 *)

%o (PARI) a(n) = round((Pi/4) * n^2); \\ _Michel Marcus_, Sep 02 2013

%o (Magma) R:= RealField(20); [Round(Pi(R)*n^2/4): n in [1..50]]; // _G. C. Greubel_, Oct 12 2019

%o (Sage) [round(pi*n^2/4) for n in (1..50)] # _G. C. Greubel_, Oct 12 2019

%o (GAP) List([1..50], n-> Int(Round(Atan(1.0)*n^2)) ); # _G. C. Greubel_, Oct 12 2019

%Y Approximation for A051233.

%K easy,nonn

%O 1,2

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