A255575 a(n) = floor(((sqrt(sqrt(3))^3)/sqrt(Pi))^n).

1, 1, 1, 2, 2, 3, 4, 5, 7, 9, 12, 15, 20, 26, 33, 43, 56, 72, 92, 119, 153, 197, 253, 325, 419, 539, 693, 891, 1146, 1474, 1896, 2439, 3136, 4034, 5188, 6672, 8581, 11036, 14194, 18254, 23476, 30192, 38830, 49938, 64225, 82598, 106227, 136616, 175698, 225961, 290603, 373737

Offset

0,4

Comments

Inspired by A255405, but starting with a unit circle and an equilateral triangle whose area is equal to Pi.

a(n) is the nested circle curvature (rounded down) after n iterations. See illustration in the links.

Links

G. C. Greubel, Table of n, a(n) for n = 0..5000

Kival Ngaokrajang, Illustration of initial terms

Formula

a(n) = floor(((sqrt(sqrt(3))^3)/sqrt(Pi))^n).

Maple

A255575:=n->floor(((sqrt(sqrt(3))^3)/sqrt(Pi))^n): seq(A255575(n), n=0..70); # Wesley Ivan Hurt, Apr 28 2017

Mathematica

Table[Floor[(Sqrt[Sqrt[3]]^3/Sqrt[Pi])^n], {n, 51}] (* Michael De Vlieger, Feb 25 2015 *)

Prog

(PARI){for(n=0, 100, a=floor(((sqrt(sqrt(3))^3)/sqrt(Pi))^n); print1(a, ", "))}

Crossrefs

Cf. A255405.

Sequence in context: A225500 A064651 A094991 * A225501 A117298 A369571

Adjacent sequences: A255572 A255573 A255574 * A255576 A255577 A255578

Keyword

nonn,easy

Author

Kival Ngaokrajang, Feb 25 2015

Status

approved