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%I #17 Sep 08 2022 08:46:00
%S 5,33,257,2049,16385,131073,1048577,8388609,67108865,536870913,
%T 4294967297,34359738369,274877906945,2199023255553,17592186044417,
%U 140737488355329,1125899906842625,9007199254740993,72057594037927937
%N 4*8^n+1.
%C An Engel expansion of 2 to the base 8 as defined in A181565, with the associated series expansion 2 = 8/5 + 8^2/(5*33) + 8^3/(5*33*257) + 8^4/(5*33*257*2049) + .... Cf. A087289 and A199493. - _Peter Bala_, Oct 29 2013
%H Vincenzo Librandi, <a href="/A199552/b199552.txt">Table of n, a(n) for n = 0..1000</a>
%H <a href="/index/Rec">Index entries for linear recurrences with constant coefficients</a>, signature (9,-8).
%F a(n) = 8*a(n-1)-7.
%F a(n) = 9*a(n-1)-8*a(n-2).
%F G.f.: (5-12*x)/((1-x)*(1-8*x)).
%t 4*8^Range[0,20]+1 (* or *) LinearRecurrence[{9,-8},{5,33},20] (* _Harvey P. Dale_, Mar 18 2018 *)
%o (Magma) [4*8^n+1: n in [0..30]];
%Y A087289, A199493.
%K nonn,easy
%O 0,1
%A _Vincenzo Librandi_, Nov 08 2011
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