A093581 Numerators of odd moments in the distribution of chord lengths for picked at random on the circumference of a unit circle.

4, 32, 512, 4096, 131072, 1048576, 16777216, 134217728, 8589934592, 68719476736, 1099511627776, 8796093022208, 281474976710656, 2251799813685248, 36028797018963968, 288230376151711744

Offset: 1

Author

Eric W. Weisstein, Apr 01 2004

Keywords

• nonn
• frac

Comments

Presumably this is the same as A102557? - Andrew S. Plewe, Apr 18 2007

A102557(n) equals a(n) for n <= 55000. - G. C. Greubel, Oct 20 2024

Examples

			1, 4/Pi, 2, 32/(3*Pi), 6, 512/(15*Pi), 20, 4096/(35*Pi), ...
		

Links

• G. C. Greubel, Table of n, a(n) for n = 1..828
• Eric Weisstein's World of Mathematics, Circle Line Picking

Crossrefs

Cf. A000984, A001803, A061549, A102557.

Denominators are A001803*Pi.

Programs

Magma

A093581:= func< n | Power(2, 4*n-2-(&+Intseq(2*(n-1), 2))) >;
[A093581(n): n in [1..30]]; // G. C. Greubel, Oct 20 2024

Mathematica

Table[Power[2, 4*n-2 - DigitCount[n-1,2,1]], {n, 30}] (* G. C. Greubel, Oct 20 2024 *)

SageMath

def A093581(n): return pow(2, 4*n-2 - sum((2*n-2).digits(2)))
[A093581(n) for n in range(1,31)] # G. C. Greubel, Oct 20 2024

Formula

a(n) = 4*A061549(n-1).