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A029858
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a(n) = (3^n - 3)/2.
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28
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0, 3, 12, 39, 120, 363, 1092, 3279, 9840, 29523, 88572, 265719, 797160, 2391483, 7174452, 21523359, 64570080, 193710243, 581130732, 1743392199, 5230176600, 15690529803, 47071589412, 141214768239
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OFFSET
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1,2
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COMMENTS
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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 greatest number of identical weights among 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 only needs to be identified, the sequence starts 4, 13, 40 and is A003462 (3^n - 1)/2, n > 1. - Tanya Khovanova, Dec 11 2006; corrected by Samuel E. Rhoads, Apr 18 2016
Binomial transform yields A134057. Inverse binomial transform yields A062510 with one additional 0 in front. - R. J. Mathar, Jun 18 2008
Numbers k where the recurrence s(0)=0, if s(k-1) >= k then s(k) = s(k-1) - k otherwise s(k) = s(k-1) + k produces s(k) = 0. - Hugo Pfoertner, Jan 05 2012
For n > 1: A008344(a(n)) = a(n). - Reinhard Zumkeller, May 09 2012
Also the number of edges in the (n-1)-Hanoi graph. - Eric W. Weisstein, Jun 18 2017
The number of degree 4 vertices in the n-Sierpinski triangle graph. - Allan Bickle, Jul 30 2020
Also the number of minimum vertex cuts in the n-Apollonian network. - Eric W. Weisstein, Dec 20 2020
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LINKS
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Vincenzo Librandi, Table of n, a(n) for n = 1..300
A. Born, C. A. J. Hukrnes, and G. J. Woeginger, How to detect a counterfeit coin: adaptive versus non-adaptive solutions, Inf. Proc. Lett. 86 (2003) 137-141.
G. Darby, The Counterfeit Coin
L. Halbeisen and N. Hungerbuhler, The general counterfeit coin problem, Discr. Math 147 (1-3) (1995) 139-150, Theorem 1 with b=1.
B. Manvel, Counterfeit coin problems, Math. Mag. 50 (2) (1977) 90-92, theorem 2.
A. Stenger and J. Wert, The Twelve Coins (or Twelve bags of Gold)
Eric Weisstein's World of Mathematics, Apollonian Network
Eric Weisstein's World of Mathematics, Edge Count
Eric Weisstein's World of Mathematics, Hanoi Graph
Eric Weisstein's World of Mathematics, Minimum Vertex Cut
Index entries for linear recurrences with constant coefficients, signature (4,-3).
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FORMULA
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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). - Vincenzo Librandi, Nov 18 2010
a(n) = 3*A003462(n-1). - R. J. Mathar, Sep 10 2015
E.g.f.: 3*(-1 + exp(2*x))*exp(x)/2. - Ilya Gutkovskiy, Apr 19 2016
a(n) = A067771(n) - 3. - Allan Bickle, Jul 30 2020
a(n) = sigma(A008776(n-2)) for n>=2. - Flávio V. Fernandes, Apr 20 2021
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MAPLE
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a:=n->sum(3^j, j=1..n): seq(a(n), n=0..23); # Zerinvary Lajos, Jun 27 2007
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MATHEMATICA
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Table[(3^n - 3)/2, {n, 24}] (* Alonso del Arte, Dec 29 2014 *)
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PROG
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(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
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CROSSREFS
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Cf. A055154, A003462, A007051, A034472, A024023, A067771.
Cf. A000203, A008776.
Sequence in context: A341712 A261384 A055294 * A123109 A240806 A242587
Adjacent sequences: A029855 A029856 A029857 * A029859 A029860 A029861
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KEYWORD
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nonn,easy
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AUTHOR
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Christian G. Bower
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EXTENSIONS
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Corrected by T. D. Noe, Nov 07 2006
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STATUS
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approved
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