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%I #19 Jun 29 2023 11:26:13
%S 27,216,1728,13824,110592,884736,7077888,56623104,452984832,
%T 3623878656,28991029248,231928233984,1855425871872,14843406974976,
%U 118747255799808,949978046398464,7599824371187712,60798594969501696
%N a(n) = 27*8^n.
%C 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).
%H <a href="/index/Rec#order_01">Index entries for linear recurrences with constant coefficients</a>, signature (8).
%F a(n) = 27*8^n = 2^3n + 2^(3n+1) + 2^(3n+3) + 2^(3n+4).
%F a(n) = 8*a(n-1), n>0; a(0)=27.
%F G.f.: 27/(1-8*x).
%F E.g.f.: 27*exp(8*x).
%F a(n) = 27*A001018(n). - _Michel Marcus_, Apr 26 2016
%t nmax=120; 27*8^Range[0, nmax]
%o (PARI) a(n) = 27*8^n; \\ _Michel Marcus_, Apr 27 2016
%Y Cf. A001018, A002063.
%K nonn,easy
%O 0,1
%A _Andres Cicuttin_, Apr 26 2016