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%I #24 Mar 20 2023 05:07:57
%S 5,13,37,109,325,973,2917,8749,26245,78733,236197,708589,2125765,
%T 6377293,19131877,57395629,172186885,516560653,1549681957,4649045869,
%U 13947137605,41841412813,125524238437,376572715309,1129718145925,3389154437773
%N a(n) = 4*3^n+1.
%C An Engel expansion of 3/4 to the base 3 as defined in A181565, with the associated series expansion 3/4 = 3/5 + 3^2/(5*13) + 3^3/(5*13*37) + 3^4/(5*13*37*109) + .... - _Peter Bala_, Oct 29 2013
%H Vincenzo Librandi, <a href="/A199108/b199108.txt">Table of n, a(n) for n = 0..1000</a>
%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (4,-3).
%F a(n) = 3*a(n-1)-2.
%F a(n) = 4*a(n-1)-3*a(n-2).
%F G.f.: (5-7*x)/((1-x)*(1-3*x)). - _Bruno Berselli_, Nov 03 2011
%t 4*3^Range[0,30]+1 (* or *) LinearRecurrence[{4,-3},{5,13},30] (* or *) NestList[3#-2&,5,30] (* _Harvey P. Dale_, Mar 01 2012 *)
%o (Magma) [4*3^n+1 : n in [0..30]]
%Y Cf. A181565.
%K nonn,easy
%O 0,1
%A _Vincenzo Librandi_, Nov 03 2011
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