0,2

Apart from leading term (which should really be 3/2), same as A055010.

Binomial transform of A040001. Inverse binomial transform of A053156.

a(n) = A105728(n+1,2). - Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Apr 18 2005

a(n) = number of partitions pi of [n+1] (in standard increasing form) such that the permutation Flatten[pi] avoids the patterns 2-1-3 and 3-1-2. Example: a(3)=11 counts all 15 partitions of [4] except 13/24, 13/2/4 which contain a 2-1-3 and 14/23, 14/2/3 which contain a 3-1-2. Here "standard increasing form" means the entries are increasing in each block and the blocks are arranged in increasing order of their first entries. - David Callan (callan(AT)stat.wisc.edu), Jul 22 2008

Eric Weisstein's World of Mathematics, Mycielski Graph [From Eric W. Weisstein (eric(AT)weisstein.com), Nov 24 2008]

a(n)=(3*2^n-2+0^n)/2. G.f.: (1-x+x^2)/((1-x)(1-2x)). E.g.f.: (3exp(2x)-2exp(x)+exp(0))/2

a(0) = 1, a(n) = sum of all previous terms + n. - Amarnath Murthy (amarnath_murthy(AT)yahoo.com), Jun 20 2004

Row sums of triangle A133567 - Gary W. Adamson (qntmpkt(AT)yahoo.com), Sep 16 2007

Row sums of triangle A135226 - Gary W. Adamson (qntmpkt(AT)yahoo.com), Nov 23 2007

a(0)=(3*2^0-2+0^0)/2=2/2=1 (use 0^0=1).

seq(ceil((2^i+2^(i+1)-2)/2), i=0..31); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Oct 02 2007

a[1] = 2; a[n_] := 2a[n - 1] + 1; Table[ a[n], {n, 31}] (from Robert G. Wilson v May 04 2004)

Essentially the same as A055010 and A052940.

Cf. A133567.

Cf. A135226.

easy,nonn,new

Paul Barry (pbarry(AT)wit.ie), Apr 27 2003

The generating function corrected by Martin Griffiths (griffm(AT)essex.ac.uk), Dec 01 2009