0,6

a(n) = b(n)/c(n) where b(n) = A001405(n+1)-A001405(n), c(n) = GCD[A001405(n+1), A001405(n)]

Also the minimal number of disjoint edge-paths into which the complete graph on n edges can be partitioned - Felix Goldberg (felixg(AT)tx.technion.ac.il), Jan 19 2001

For n>=2, number of partitions of n-2 into parts that are distinct mod 2. - Giovanni Resta (g.resta(AT)iit.cnr.it), Feb 06 2006

Sequence starting with a(3) obeys the rule "smallest positive value such that the ordered pair a(n-1),a(n) has not occurred previously", or the rule "smallest positive value such that the ratio a(n-1)/a(n) has not occurred previously". The same subsequence has its ordinal transform equal to itself, shifted left. (The ordinal transform has as its n-th term the number of values in a(1),...,a(n) that are equal to a(n).) - Franklin T. Adams-Watters (FrankTAW(AT)Netscape.net), Dec 13 2006

a(n) = (n+3)/4+(1-n)*(-1)^n/4 - Paul Barry (pbarry(AT)wit.ie), Mar 21 2003, corrected by Hieronymus Fischer (Hieronymus.Fischer(AT)gmx.de), Sep 25 2007

a(n) =(a(n-2)+a(n-3))/a(n-1).

G.f. : (1-x^2+x^3)/((1+x)^2(1-x)^2); a(n)=2a(n-2)-a(n-4); a(n)=0^n+sum{k=0..floor((n-2)/2), binomial(n-k-2, k)binomial(1, n-2k-2)}. - Paul Barry (pbarry(AT)wit.ie), Oct 21 2004

a(n)=gcd(n-1, floor((n-1)/2)) - Paul Barry (pbarry(AT)wit.ie), May 02 2005

a(n)=binomial((2n-3)/4-(-1)^n/4,(1-(-1)^n)/2); - Paul Barry (pbarry(AT)wit.ie), Jun 29 2006

n=13, C(13,6)-C(12,6)=792, GCD[C(13,6),C(12,6)]=132, the quotient is 6=Floor[13/2]; n=12 C(12,6)-C(11,5)=924-462=462,GCD[C(12,6),C(11,5)]=462, the quotient is 1.

Cf. A001405, A007879, A059222, A000035, A027656, A037952.

Cf. A067992.

Sequence in context: A077609 A077610 A007879 this_sequence A152271 A133622 A158416

Adjacent sequences: A057976 A057977 A057978 this_sequence A057980 A057981 A057982

nonn

Labos E. (labos(AT)ana.sote.hu), Nov 13 2000