1,2

Necklaces with n beads that are the same when turned over.

The subset {a(1),...,a(2k)} contains all proper divisors of 3*2^k. - Ralf Stephan, Jun 02 2003

Let k = any nonnegative integer, and j = 0 or 1. Then n+1 = 2k + 3j, and a(n) = 2^k*3^j. - Andras Erszegi (erszegi.andras(AT)chello.hu), Jul 30 2005

Smallest number having not less prime factors than any predecessor, a(0)=1; A110654(n)=A001222(a(n)); complement of A116451. - Reinhard Zumkeller (reinhard.zumkeller(AT)lhsystems.com), Feb 16 2006

A093873(a(n)) = 1. - Reinhard Zumkeller (reinhard.zumkeller(AT)lhsystems.com), Oct 13 2006

Index entries for sequences related to necklaces

a(n)=2*A000029(n)-A000031(n).

For n>2 a(n)=2a(n-2); for n>3 a(n)=a(n-1)*a(n-2)/a(n-3). G.f.: (1+x)^2/(1-2*x^2). - Henry Bottomley (se16(AT)btinternet.com), Jul 15 2001, corrected May 04 2007

a(0)=1, a(1)=1 and a(n) = a(n-2) * ( floor(a(n-1)/a(n-2)) + 1 ) - Benoit Cloitre (benoit7848c(AT)orange.fr), Aug 13 2002

(3/4+sqrt(1/2))*sqrt(2)^n + (3/4-sqrt(1/2))*(-sqrt(2))^n. a(0)=1, a(2n) = a(n-1)*a(n), a(2n+1) = a(n) + 2^floor((n-1)/2). Ralf Stephan, Apr 16 2003

Binomial transform is A048739. - Paul Barry (pbarry(AT)wit.ie), Apr 23 2004

E.g.f.: (cosh(x/sqrt(2))+sqrt(2)sinh(x/sqrt(2)))^2.

a(1) = 1; a(n+1) = a(n) + A000010(a(n)) - Stefan Steinerberger (stefan.steinerberger(AT)gmail.com), Dec 20 2007

u(2)=1, v(2)=1, u(n)=2*v(n-1), v(n)=u(n-1), a(n)=u(n)+v(n) - Jaume Oliver (joliverlafont(AT)gmail.com), May 21 2008

(PARI) a(n)=if(n<1, n==0, 2^(n\2)*if(n%2, 2, 3/2))

Cf. A056493, A038754, A063759. Union of A000079 and A007283.

First differences are in A016116(n-1).

Cf. A082125.

Cf. A094958.

Sequence in context: A064428 A052810 A079647 this_sequence A018635 A018425 A018328

Adjacent sequences: A029741 A029742 A029743 this_sequence A029745 A029746 A029747

nonn,easy

njas

Corrected and extended by Joe Keane (jgk(AT)jgk.org), Feb 20 2000