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%I #30 Sep 08 2022 08:45:59
%S 12,25,51,103,207,415,831,1663,3327,6655,13311,26623,53247,106495,
%T 212991,425983,851967,1703935,3407871,6815743,13631487,27262975,
%U 54525951,109051903,218103807,436207615,872415231,1744830463,3489660927,6979321855,13958643711
%N a(n) = 13*2^n-1.
%C a(n) + a(n-1)^2 = (a(n-1)+1)^2. - _Vincenzo Librandi_, Mar 24 2013
%H Vincenzo Librandi, <a href="/A198274/b198274.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 (3,-2).
%F a(n+1) = 2*a(n) + 1.
%F G.f.: ( 12-11*x ) / ( (2*x-1)*(x-1) ). - _R. J. Mathar_, Oct 25 2011
%e a(2) = 13*2^2-1 = 51.
%t Table[13 2^n - 1, {n, 0, 30}] (* _Vincenzo Librandi_, Mar 24 2013 *)
%t LinearRecurrence[{3,-2},{12,25},40] (* _Harvey P. Dale_, Feb 06 2019 *)
%o (BASIC) for j = 0 to 30 : print str$((13*2^j)-1)+", "; : next j
%o (Magma) [13*2^n-1: n in [0..30]]; // _Vincenzo Librandi_, Oct 28 2011
%o (PARI) a(n) = 13*2^n-1; \\ _Michel Marcus_, Jan 17 2016
%Y Cf. A005029, A086224.
%K nonn,easy
%O 0,1
%A _Jeremy Gardiner_, Oct 23 2011
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