1,3

Starting from the 4th term, every succeeding term is twice the preceding term. I.e. a(n+1) = 2a(n).

Number of binary words of length n-2 that do not start with 01 (n>=2). Example: a(5)=6 because we have 000,001,100,101,110 and 111. Except for the initial term, column 0 of A119440. - Emeric Deutsch (deutsch(AT)duke.poly.edu), May 19 2006

a(n) written in base 2: a(1) = 1, a(2) = 1, a(3) = 10, a(n) for n >= 4: 11, 110, 11000, 110000, ..., i.e.: 2 times 1, (n-4) times 0 (see A003953(n-3). [From Jaroslav Krizek (jaroslav.krizek(AT)atlas.cz), Aug 17 2009]

G.f.: x(1-x-x^3)/(1-2x) - Paul Barry (pbarry(AT)wit.ie), Feb 17 2005

a(n)=3*2^(n-4) for n>=4; a(1)=a(2)=1, a(3)=2. - Emeric Deutsch (deutsch(AT)duke.poly.edu), May 19 2006

a(n) = 3*2^(n-4) = 2^(n-4) + 2^(n-3) for n >= 4. [From Jaroslav Krizek (jaroslav.krizek(AT)atlas.cz), Aug 17 2009]

a(0) = 1, a(2) = 1, a(3) = 2, for n >= 4: a(n) = Sum_(i=2...n-1) a(i). [From Jaroslav Krizek (jaroslav.krizek(AT)atlas.cz), Nov 16 2009]

a:=proc(n) if n=1 or n=2 then 1 elif n=3 then 2 else 3*2^(n-4) fi end: seq(a(n), n=1..37); - Emeric Deutsch (deutsch(AT)duke.poly.edu), May 19 2006

Table[ Ceiling[3*2^(n - 4)], {n, 34}] (* or *)

Rest@CoefficientList[Series[x(1 - x - x^3)/(1 - 2x), {x, 0, 33}], x] (from Robert G. Wilson v (rgwv(at)rgwv.com), Jul 08 2006)

Cf. A119440.

Sequence in context: A124313 A049890 A042950 this_sequence A110164 A035055 A119559

Adjacent sequences: A098008 A098009 A098010 this_sequence A098012 A098013 A098014

nonn,new

Ray G. Opao (1260(AT)email.com), Sep 09 2004

More terms from Emeric Deutsch (deutsch(AT)duke.poly.edu), May 19 2006