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A042950
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Row sums of the Lucas triangle A029635.
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31
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2, 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
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OFFSET
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0,1
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COMMENTS
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Map a binary sequence b=[ b_1,...] to a binary sequence c=[ c_1,...] so that C = 1/Product((1-x^i)^c_i == 1+Sum b_i*x^i mod 2.
This produces 2 new sequences: d={i:c_i=1} and e=[ 1,e_1,... ] where C = 1 + Sum e_i*x^i.
This sequence is d when b=[ 0,1,1,1,1,...].
Number of rises after n+1 iterations of morphism A007413.
a(n) written in base 2: a(0) = 10, a(n) for n >= 1: 11, 110, 11000, 110000, ..., i.e.: 2 times 1, (n-1) times 0 (see A003953(n)). - Jaroslav Krizek, Aug 17 2009
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LINKS
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FORMULA
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G.f.: (2-x)/(1-2*x).
a(n) = 2*a(n-1), n > 1; a(0)=2, a(1)=3.
Binomial transform of 2, 1, 2, 1, 2, 1, ... = (3+(-1)^n)/2.
a(n) = (3*2^n + 0^n)/2. (End)
a(0) = 2, a(n) = 3*2^(n-1) = 2^n + 2^(n-1) for n >= 1. - Jaroslav Krizek, Aug 17 2009
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MATHEMATICA
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a[0] = 2; a[1] = 3; a[n_] := 2a[n - 1]; Table[a[n], {n, 0, 32}] (* Robert G. Wilson v, Jul 08 2006 *)
CoefficientList[Series[(2 - x)/(1 - 2x), {x, 0, 32}], x] (* Robert G. Wilson v, Jul 08 2006 *)
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PROG
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(PARI) a(n)=ceil(3*2^(n-1))
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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