A045674 - OEIS

%I #15 Sep 30 2017 14:55:05

%S 1,1,2,2,4,4,6,8,12,16,20,32,38,64,72,128,140,256,272,512,532,1024,

%T 1056,2048,2086,4096,4160,8192,8264,16384,16512,32768,32908,65536,

%U 65792,131072,131344,262144,262656,524288,524820,1048576,1049600

%N Number of 2n-bead balanced binary necklaces which are equivalent to their reverse, complement and reversed complement.

%H Andrew Howroyd, <a href="/A045674/b045674.txt">Table of n, a(n) for n = 0..200</a>

%H <a href="/index/Ne#necklaces">Index entries for sequences related to necklaces</a>

%F a(2n) = a(n) + 2^(n-1), a(2n+1) = 2^n. - _Ralf Stephan_, Nov 01 2003

%t a[0] = 1; a[n_] := a[n] = If[EvenQ[n], 2^(n/2-1) + a[n/2], 2^((n-1)/2)]; Table[a[n], {n, 0, 42}] (* _Jean-François Alcover_, Sep 30 2017 *)

%o (PARI) a(n) = if(n<1, n==0, my(t=0,r=n); while(r%2==0, r=r/2; t+=2^(r-1)); t + 2^(r\2)); \\ _Andrew Howroyd_, Sep 29 2017

%Y Cf. A045654.

%K nonn

%O 0,3

%A _David W. Wilson_