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27, 216, 1728, 13824, 110592, 884736, 7077888, 56623104, 452984832, 3623878656, 28991029248, 231928233984, 1855425871872, 14843406974976, 118747255799808, 949978046398464, 7599824371187712, 60798594969501696
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OFFSET
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0,1
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COMMENTS
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a(n) are cubes that can be expressed as sum of exactly four distinct powers of two: a(n)=2^3n + 2^(3n+1) + 2^(3n+3) + 2^(3n+4). For example a(0) = 2^0 + 2^1 + 2^3 + 2^4 = 1 + 2 + 8 + 16 = 27. It is conjectured the a(n) are the only cubes that can be expressed as sum of exactly four distinct nonnegative powers of two (tested on cubes up to (10^7)^3).
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LINKS
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Table of n, a(n) for n=0..17.
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FORMULA
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a(n) = 27*8^n = 2^3n + 2^(3n+1) + 2^(3n+3) + 2^(3n+4).
a(n) = 8*a(n-1), n>0; a(0)=27.
G.f.: 27/(1-8*x).
E.g.f.: 27*exp(8*x).
a(n) = 27*A001018(n). - Michel Marcus, Apr 26 2016
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MATHEMATICA
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nmax=120; 27*8^Range[0, nmax]
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PROG
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(PARI) a(n) = 27*8^n; \\ Michel Marcus, Apr 27 2016
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CROSSREFS
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Cf. A001018, A002063.
Sequence in context: A224013 A059827 A117688 * A107054 A160441 A222994
Adjacent sequences: A272339 A272340 A272341 * A272343 A272344 A272345
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KEYWORD
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nonn,easy
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AUTHOR
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Andres Cicuttin, Apr 26 2016
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STATUS
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approved
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