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a(n) = ceiling(n^3*(Pi/2)).
1

%I #23 May 06 2022 13:13:51

%S 2,13,43,101,197,340,539,805,1146,1571,2091,2715,3452,4311,5302,6434,

%T 7718,9161,10775,12567,14548,16726,19112,21715,24544,27609,30918,

%U 34483,38311,42412,46796,51472,56450,61739,67348,73288,79566,86193,93179,100531

%N a(n) = ceiling(n^3*(Pi/2)).

%C a(n) is the ceiling of the area of a square with diagonal n times the circumference of a circle with diameter n. - _Wesley Ivan Hurt_, Oct 03 2014

%C a(n) is also the ceiling of the volume of a cylinder with radius n and height n/2. Equivalently, a(n) is the ceiling of the volume of a cylinder with diameter n and height 2*n. - _Derek Orr_, Oct 03 2014

%p A248198:=n->ceil(n^3*(Pi/2)): seq(A248198(n), n=1..40); # _Wesley Ivan Hurt_, Oct 03 2014

%t Table[Ceiling[n^3*(Pi/2)], {n, 40}] (* _Wesley Ivan Hurt_, Oct 03 2014 *)

%o (Java) int a(int n) {return (int) Math.ceil(Math.pow(n, 3)*Math.PI/(2)); }

%o (PARI) vector(100,n,ceil(n^3*Pi/2)) \\ _Derek Orr_, Oct 03 2014

%Y Cf. A228391 (similar, with floor).

%K nonn,easy

%O 1,1

%A _Juliann Barbella_, Oct 03 2014