A115120 - OEIS

%I #11 Aug 28 2019 08:15:17

%S 0,0,1,1,2,1,4,1,8,3,17,1,56,1,134,18,440,1,1434,1,4758,135,16160,1,

%T 57254,16,200475,1387,718152,1,2591800,1,9398520,16161,34324175,148,

%U 126125330,1,465093572,200476,1723176740,1,6408642359,1,23910576236,2588402,89494164974,1,335923316982,133,1264107421202

%N Number of imprimitive (periodic) 2n-bead black-white reversible necklaces with n black beads.

%C a(p)=1 for prime p.

%F a(n) = A005648(n) - A045628(n).

%t A005648[0] = 1; A005648[n_] := (1/2)(Binomial[2 Quotient[n, 2], Quotient[n, 2]] + DivisorSum[n, EulerPhi[#] Binomial[2n/#, n/#] &]/(2n));

%t A045628[n_] := If[n == 0, 1, Sum[MoebiusMu[n/d] (2n Binomial[2 Quotient[d, 2], Quotient[d, 2]] + Binomial[2d, d]), {d, Divisors[n]}]/(4n)];

%t a[n_] := A005648[n] - A045628[n];

%t Table[a[n], {n, 0, 50}] (* _Jean-François Alcover_, Aug 28 2019 *)

%K easy,nonn

%O 0,5

%A _Valery A. Liskovets_, Jan 17 2006

%E More terms from _Jean-François Alcover_, Aug 28 2019