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

1,1

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

Links

G. C. Greubel, Table of n, a(n) for n = 1..828

Eric Weisstein's World of Mathematics, Circle Line Picking

Formula

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

Example

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

Mathematica

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

Prog

(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
(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

Crossrefs

Cf. A000984, A001803, A061549, A102557.

Denominators are A001803*Pi.

Sequence in context: A034663 A192501 A192487 * A102557 A144935 A153511

Adjacent sequences: A093578 A093579 A093580 * A093582 A093583 A093584

Keyword

nonn,frac

Author

Eric W. Weisstein, Apr 01 2004

Status

approved