1,2

Also the number of 2-block covers of a labeled n-set. a(n) = A055154(n,2). Generally, number of k-block covers of a labeled n-set is T(n,k) = (1/k!)*Sum_{i = 1..k + 1} stirling1(k + 1,i)*(2^(i - 1) - 1)^n. In particular, T(n,2) = (1/2!)*(3^n - 3), T(n,3) = (1/3!)*(7^n - 6*3^n + 11), T(n,4) = (1/4)!*(15^n - 10*7^n + 35*3^n - 50),... - Vladeta Jovovic (vladeta(AT)eunet.rs), Jan 19 2001

Conjectured to be the number of integers from 0 to 10^(n-1) - 1 that lack 0, 1, 2, 3, 4, 5 and 6 as a digit. - Alexandre Wajnberg (alexandre.wajnberg(AT)ulb.ac.be), Apr 25 2005. This is easily verified to be true. - Renzo Benedetti, Sep 25 2008

Number of monic irreducible polynomials of degree 1 in GF(3)[x1,...,xn]. - Max Alekseyev (maxale(AT)gmail.com), Jan 23 2006

Also, the least number of identical weights amongst which an odd one can be identified and it can be decided if the odd one is heavier or lighter, using n weighings with a comparing balance. (If the odd one needs to be only identified, the sequence starts 1, 4, 13 and is A003462 (3^n - 1)/2. - Tanya Khovanova, Dec 11 2006.)

Binomial transform yields A134057. Inverse binomial transform yields A062510 with one additional 0 in front. - R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Jun 18 2008

G. Darby, The Counterfeit Coin

A. Stenger and J. Wert, The Twelve Coins (or Twelve bags of Gold)

Eric Weisstein's World of Mathematics, Hanoi Graph

a(n) = 3a(n-1) + 3. - Alexandre Wajnberg (alexandre.wajnberg(AT)ulb.ac.be), Apr 25 2005

O.g.f: 3x^2/((1-x)(1-3x)). - R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Jun 18 2008

a(n)=3^n+a(n-1) (with a(0)=0) [From Vincenzo Librandi (vincenzo.librandi(AT)tin.it), Nov 30 2009]

For n=1, a(1)=3+0=3; n=2, a(2)=3^2+3=12; n=3, a(3)=3^3+12=39 [From Vincenzo Librandi (vincenzo.librandi(AT)tin.it), Nov 30 2009]

a:=n->sum (3^j, j=1..n): seq(a(n), n=0..23); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Jun 27 2007

with(finance):seq(add(futurevalue( 3, 2, k), k=0..n), n=-1..22); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Jun 20 2008

a=0; lst={a}; Do[a=a*3+3; AppendTo[lst, a], {n, 0, 5!}]; lst [From Vladimir Orlovsky (4vladimir(AT)gmail.com), Dec 25 2008]

Cf. A055154.

Cf. A003462, A007051, A034472, A024023, A067771 [From Vladimir Orlovsky (4vladimir(AT)gmail.com), Dec 25 2008]

Sequence in context: A048246 A129014 A055294 this_sequence A123109 A110153 A122994

Adjacent sequences: A029855 A029856 A029857 this_sequence A029859 A029860 A029861

nonn,new

Christian Bower (bowerc(AT)usa.net)

Corrected by T. D. Noe (noe(AT)sspectra.com), Nov 07 2006