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

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

Sequence in context: A060153 A086219 A055010 this_sequence A081973 A055496 A105120

Adjacent sequences: A083326 A083327 A083328 this_sequence A083330 A083331 A083332

easy,nonn

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