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A029858 (3^n-3)/2. 23
0, 3, 12, 39, 120, 363, 1092, 3279, 9840, 29523, 88572, 265719, 797160, 2391483, 7174452, 21523359, 64570080, 193710243, 581130732, 1743392199, 5230176600, 15690529803, 47071589412, 141214768239 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

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, 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, 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, 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, Jun 18 2008

Numbers n where the recurrence s(0)=0, if s(n-1)>=n then s(n)=s(n-1)-n else s(n)=s(n-1)+n produces s(n)=0. [From Hugo Pfoertner, Jan 05 2012]

For n > 1: A008344(a(n)) = a(n). [Reinhard Zumkeller, May 09 2012]

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 1..300

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

Index to sequences with linear recurrences with constant coefficients, signature (4,-3).

FORMULA

a(n) = 3*a(n-1) + 3. - Alexandre Wajnberg, Apr 25 2005

O.g.f: 3*x^2/((1-x)*(1-3*x)). - R. J. Mathar, Jun 18 2008

a(n)=3^(n-1)+a(n-1) (with a(1)=0) [From Vincenzo Librandi, Nov 18 2010]

MAPLE

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

MATHEMATICA

a=0; lst={a}; Do[a=a*3+3; AppendTo[lst, a], {n, 0, 5!}]; lst [From Vladimir Joseph Stephan Orlovsky, Dec 25 2008]

PROG

(MAGMA)[(3^n-3)/2: n in [1..30]]; // Vincenzo Librandi, Jun 05 2011

(PARI) a(n)=(3^n-3)\2 \\ Charles R Greathouse IV, Apr 17 2012

(Haskell)

a029858 = (`div` 2) . (subtract 3) . (3 ^)

a029858_list = iterate ((+ 3) . (* 3)) 0

-- Reinhard Zumkeller, May 09 2012

CROSSREFS

Cf. A055154, A003462, A007051, A034472, A024023, A067771.

Sequence in context: A222643 A129014 A055294 * A123109 A240806 A242587

Adjacent sequences:  A029855 A029856 A029857 * A029859 A029860 A029861

KEYWORD

nonn,easy

AUTHOR

Christian G. Bower

EXTENSIONS

Corrected by T. D. Noe, Nov 07 2006

STATUS

approved

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Last modified October 30 11:35 EDT 2014. Contains 248798 sequences.