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A007283
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3*2^n.
(Formerly M2561)
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106
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3, 6, 12, 24, 48, 96, 192, 384, 768, 1536, 3072, 6144, 12288, 24576, 49152, 98304, 196608, 393216, 786432, 1572864, 3145728, 6291456, 12582912, 25165824, 50331648, 100663296, 201326592, 402653184, 805306368, 1610612736, 3221225472, 6442450944, 12884901888
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OFFSET
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0,1
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COMMENTS
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Same as Pisot sequences E(3,6), L(3,6), P(3,6), T(3,6). See A008776 for definitions of Pisot sequences.
Numbers n such that P[phi[n]]=phi[P[n]], where P[x] is the largest prime-factor of x; A006530[A000010(n)]=A000010[A006530(n)]=2. - Labos E. (labos(AT)ana.sote.hu), May 07 2002
Also least number m such that 2^n is the smallest proper divisor of m which is also a suffix of m in binary representation, see A080940. - Reinhard Zumkeller, Feb 25 2003
Length of the period of the sequence Fibonacci(k) (mod 2^(n+1)). - Benoit Cloitre, Mar 12 2003
The first differences are the sequence itself. - Alexandre Wajnberg & Eric Angelini, Sep 07 2005
Subsequence of A122132. - Reinhard Zumkeller, Aug 21 2006
Apart from the first term, a subsequence of A124509. - Reinhard Zumkeller, Nov 04 2006
Total number of Latin n-dimensional hypercubes (Latin polyhedra) of order 3. - Kenji Ohkuma (k-ookuma(AT)ipa.go.jp), Jan 10 2007
Number of different ternary hypercubes of dimension n. - Edwin Soedarmadji (edwin(AT)systems.caltech.edu), Dec 10 2005
For n>=1, a(n) is equal to the number of functions f:{1,2,...,n+1}->{1,2,3} such that for fixed, different x_1, x_2,...,x_n in {1,2,...,n+1} and fixed y_1, y_2,...,y_n in {1,2,3} we have f(x_i)<>y_i, (i=1,2,...,n). - Milan Janjic, May 10 2007
3 times powers of 2. [From Omar E. Pol, Dec 16 2008]
From Jacobsthal numbers and successive differences. A001045=0,1,1,3,5,11,21,43,; A078008=1,0,2,2,6,10,22,42,; A084247 signed=-1,2,0,4,4,12,20,44,; A154879=3,-2,4,0,8,8,24,40,. For every sequence k(n), a(n)= k(n)+k(n+3).Then A001045(n)+A001045(n+3), A078008(n)+A078008(n+3), .. . [From Paul Curtz, Feb 05 2009]
a(n) written in base 2: 11, 110, 11000, 110000, ..., i.e.: 2 times 1, n times 0 (see A003953(n)). [From Jaroslav Krizek, Aug 17 2009]
a(n) = A173786(n+1,n) = A173787(n+2,n). [From Reinhard Zumkeller, Feb 28 2010]
Subsequence of A051916. [From Reinhard Zumkeller, Mar 20 2010]
Numbers containing the number 3 in their Collatz trajectories. [Reinhard Zumkeller, Feb 20 2012]
For n > 0: A216022(a(n)) = 6 and A216059(a(n)) = 7. -- Reinhard Zumkeller, Sep 01 2012
a(n-1) gives the number of ternary numbers with n digits with no two adjacent digits in common, e.g. for n=3 we have 010, 012, 020, 021, 101, 102, 120, 121, 201, 202, 210 and 212. - Jon Perry, Oct 10 2012
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REFERENCES
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T. Ito, Method, equipment, program and storage media for producing tables, Publication number JP2004-272104A, Japan Patent Office(written in Japanese, a(2)=12,a(3)=24,a(4)=48,a(5)=96,a(6)=192,a(7)=384(a(7)=284 was corrected)).
Kenji Ohkuma, Atsuhiro Yamagishi and Toru Ito, Cryptography Research Group Technical report, IT Security Center, Information-Technology Promotion Agency, JAPAN.
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
E. Soedarmadji, Latin Hypercubes and MDS Codes, preprint, 2005.
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LINKS
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Vincenzo Librandi, Table of n, a(n) for n = 0..1000
Tanya Khovanova, Recursive Sequences
Index entries for sequences related to linear recurrences with constant coefficients
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FORMULA
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G.f.: 3/(1-2*x)
a(n)=2*a(n-1), n>0; a(0)=3.
a(n) = sum(k=0, n, (-1)^(k reduced (mod 3))*C(n, k)) - Benoit Cloitre, Aug 20 2002
a(n) = A118416(n+1,2) for n>1. - Reinhard Zumkeller, Apr 27 2006
a(n)=A000079(n)+A000079(n+1). - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), May 12 2007
a(n) = A000079(n)*3. [From Omar E. Pol, Dec 16 2008]
a(n) = 2^n + 2^(n-1) for n >= 1. [From Jaroslav Krizek, Aug 17 2009]
a(n) = (A000225(n)+1)*3. - Martin Ettl, Nov 11 2012
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MATHEMATICA
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Table[3(2^n), {n, 0, 32}] (* From Alonso del Arte, Mar 24 2011 *)
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PROG
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(PARI) a(n)=3*2^n
(PARI) a(n)=3<<n \\ Charles R Greathouse IV, Oct 10 2012
(MAGMA) [3*2^n: n in [0..30]]; // Vincenzo Librandi, May 18 2011
(Haskell)
a007283 = (* 3) . (2 ^)
a007283_list = iterate (* 2) 3
-- Reinhard Zumkeller, Mar 18 2012, Feb 20 2012
(Maxima) A007283(n):=3*2^n$
makelist(A007283(n), n, 0, 30); /* Martin Ettl, Nov 11 2012 */
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CROSSREFS
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Essentially same as A003945 and A042950.
Row sums of (5, 1)-Pascal triangle A093562 and of (1, 5) Pascal triangle A096940.
Cf. A000079, A002860, A098679, A100540, A124508, A221718.
Cf. Latin squares: A000315, A002860, A003090, A040082, A003191; Latin cubes: A098843, A098846, A098679, A099321.
Subsequence of A029744.
Sequence in context: A170636 A170684 A003945 * A049942 A200463 A099844
Adjacent sequences: A007280 A007281 A007282 * A007284 A007285 A007286
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KEYWORD
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easy,nonn
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AUTHOR
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N. J. A. Sloane.
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STATUS
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approved
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