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A083233
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a(n) = (3*8^n + 0^n)/4.
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6
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1, 6, 48, 384, 3072, 24576, 196608, 1572864, 12582912, 100663296, 805306368, 6442450944, 51539607552, 412316860416, 3298534883328, 26388279066624, 211106232532992, 1688849860263936, 13510798882111488, 108086391056891904, 864691128455135232
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OFFSET
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0,2
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COMMENTS
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Binomial transform of A083232. Inverse binomial transform of A066443
Numbers n such that, except some first term, n^2 = [A000302]^3 + [A004171]^3 + [A002001]^3; e.g., 3072^2 = 64^3 + 128^3 + 192^3; 51539607552^2 = 4194304^3 + 8388608^3 + 12582912^3. - Vincenzo Librandi, Aug 08 2010
With the exception of the first term, these numbers cannot be written as the sum of two integer cubes but can be written as the sum of two positive rational cubes (i.e., 6*8^n = (17*2^n/21)^3 + (37*2^n/21)^3). - Arkadiusz Wesolowski, Aug 15 2013
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LINKS
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Table of n, a(n) for n=0..20.
Index entries for linear recurrences with constant coefficients, signature (8).
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FORMULA
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a(n) = (3*8^n + 0^n)/4.
G.f.: (1-2x)/(1-8x).
E.g.f.: (3exp(8x) + exp(0))/4.
a(0) = 1, a(n+1) = 6*8^n. - Arkadiusz Wesolowski, Aug 15 2013
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EXAMPLE
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a(0) = (3*8^0 + 0^0)/4 = 4/4 = 1 (using 0^0 = 1).
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MATHEMATICA
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Join[{1}, NestList[8#&, 6, 20]] (* Harvey P. Dale, Sep 25 2020 *)
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PROG
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(PARI) a(n)=(3*8^n+0^n)/4 \\ Charles R Greathouse IV, Oct 07 2015
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CROSSREFS
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Cf. A083234. Subsequence of A159843.
Cf. A000302, A004171, A002001.
Sequence in context: A155130 A250164 A264083 * A002918 A005399 A258790
Adjacent sequences: A083230 A083231 A083232 * A083234 A083235 A083236
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KEYWORD
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easy,nonn
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AUTHOR
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Paul Barry, Apr 23 2003
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STATUS
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approved
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