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A110593
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a(1) = 3, a(n+1) = 2*(3^n).
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5
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3, 6, 18, 54, 162, 486, 1458, 4374, 13122, 39366, 118098, 354294, 1062882, 3188646, 9565938, 28697814, 86093442, 258280326, 774840978, 2324522934, 6973568802, 20920706406, 62762119218, 188286357654, 564859072962, 1694577218886
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OFFSET
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1,1
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COMMENTS
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Since A081604 = "string-length of ternary representation of n", we have A081604 = A110593 # n. This is in terms of the repetition convolution operator #, where (sequence A) # (sequence B) = the sequence consisting of A(n) copies of B(n). Over the set of positive infinite integer sequences, # gives a nonassociative noncommutative groupoid (magma) with a left identity (A000012) but no right identity, where the left identity is also a right nullifier and idempotent. For any positive integer constant c, the sequence c*A000012 = (c,c,c,c,...) is also a right nullifier; for c = 1, this is A000012; for c = 3 this is A010701.
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LINKS
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G. C. Greubel, Table of n, a(n) for n = 1..1000
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FORMULA
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a(1) = 3, a(2) = 6, for n>2: a(n+1) = 3*a(n). For n>1, cumulative sum of a(n) = A000244 = powers of 3. a(n) = the number of occurrences of the integer n in A081604 = "string-length of ternary representation of n."
a(n) = A008776(n-1) for n>1. - R. J. Mathar, Apr 24 2007
G.f.: 3*x + 6*x^2/(1-3*x). - R. J. Mathar, Nov 18 2007
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MATHEMATICA
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Rest[CoefficientList[Series[3 x + 6 x^2/(1 - 3 x), {x, 0, 50}], x]] (* G. C. Greubel, Sep 01 2017 *)
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PROG
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(PARI) x='x+O('x^50); Vec(3*x + 6*x^2/(1-3*x)) \\ G. C. Greubel, Sep 01 2017
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CROSSREFS
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Cf. A000244, A081604.
Sequence in context: A148565 A112572 A089325 * A049368 A152733 A215455
Adjacent sequences: A110590 A110591 A110592 * A110594 A110595 A110596
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KEYWORD
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easy,nonn
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AUTHOR
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Jonathan Vos Post, Jul 29 2005
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STATUS
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approved
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