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%I #27 Sep 08 2022 08:45:41
%S 10,23,49,101,205,413,829,1661,3325,6653,13309,26621,53245,106493,
%T 212989,425981,851965,1703933,3407869,6815741,13631485,27262973,
%U 54525949,109051901,218103805,436207613,872415229,1744830461,3489660925,6979321853,13958643709
%N a(n) = 2*a(n-1)+3 for n > 1, a(1) = 10.
%H Vincenzo Librandi, <a href="/A156202/b156202.txt">Table of n, a(n) for n = 1..1000</a>
%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (3,-2).
%F a(n) = -3+13*2^(n-1).
%F G.f.: x*(10-7*x)/(1-3*x+2*x^2). - _Vincenzo Librandi_, May 02 2012
%F a(n) = 3*a(n-1) - 2*a(n-2). - _Vincenzo Librandi_, May 02 2012
%t LinearRecurrence[{3,-2},{10,23},30] (* _Vincenzo Librandi_, May 02 2012 *)
%t NestList[2#+3&,10,40] (* _Harvey P. Dale_, Jul 08 2019 *)
%o (Magma) I:=[10, 23]; [n le 2 select I[n] else 3*Self(n-1)-2*Self(n-2): n in [1..30]]; // _Vincenzo Librandi_, May 02 2012
%o (Python)
%o from itertools import accumulate
%o def f(an, _): return 2*an + 3
%o print(list(accumulate([10]*31, f))) # _Michael S. Branicky_, Oct 23 2021
%K nonn,easy
%O 1,1
%A _Vincenzo Librandi_, Feb 08 2009
%E Definition and closed form corrected by _Paolo P. Lava_, Feb 13 2009
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