A093581 - OEIS

%I #16 Oct 20 2024 13:54:50

%S 4,32,512,4096,131072,1048576,16777216,134217728,8589934592,

%T 68719476736,1099511627776,8796093022208,281474976710656,

%U 2251799813685248,36028797018963968,288230376151711744

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

%C Presumably this is the same as A102557? - _Andrew S. Plewe_, Apr 18 2007

%C A102557(n) equals a(n) for n <= 55000. - _G. C. Greubel_, Oct 20 2024

%H G. C. Greubel, <a href="/A093581/b093581.txt">Table of n, a(n) for n = 1..828</a>

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/CircleLinePicking.html">Circle Line Picking</a>

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

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

%t Table[Power[2, 4*n-2 - DigitCount[n-1,2,1]], {n, 30}] (* _G. C. Greubel_, Oct 20 2024 *)

%o (Magma)

%o A093581:= func< n | Power(2, 4*n-2-(&+Intseq(2*(n-1), 2))) >;

%o [A093581(n): n in [1..30]]; // _G. C. Greubel_, Oct 20 2024

%o (SageMath)

%o def A093581(n): return pow(2, 4*n-2 - sum((2*n-2).digits(2)))

%o [A093581(n) for n in range(1,31)] # _G. C. Greubel_, Oct 20 2024

%Y Cf. A000984, A001803, A061549, A102557.

%Y Denominators are A001803*Pi.

%K nonn,frac

%O 1,1

%A _Eric W. Weisstein_, Apr 01 2004