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%I #26 Sep 08 2022 08:45:43
%S 1,5,18,67,260,1029,4102,16391,65544,262153,1048586,4194315,16777228,
%T 67108877,268435470,1073741839,4294967312,17179869201,68719476754,
%U 274877906963,1099511627796,4398046511125,17592186044438,70368744177687
%N a(n) = 4^n + n.
%H Vincenzo Librandi, <a href="/A158879/b158879.txt">Table of n, a(n) for n = 0..300</a>
%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (6,-9,4).
%F G.f.: (1 - x - 3*x^2)/((1-4*x)*(1-x)^2). - _R. J. Mathar_, Mar 29 2009
%F a(n) = 6*a(n-1) -9*a(n-2) +4*a(n-3). - _R. J. Mathar_, Mar 29 2009
%F E.g.f.: x*exp(x) + exp(4*x). - _G. C. Greubel_, Mar 04 2020
%e a(0)=4^0+0 = 1, a(1)=4^1+1 = 5, a(2)=4^2+2 = 18, a(3)=4^3+3 = 67, ...
%p seq( 4^n+n, n=0..30); # _G. C. Greubel_, Mar 04 2020
%t Table[4^n+n,{n,0,40}] (* _Vladimir Joseph Stephan Orlovsky_, May 19 2011 *)
%t CoefficientList[Series[(1-x-3x^2)/((1-4x)(1-x)^2), {x, 0, 30}], x] (* _Vincenzo Librandi_, Jun 16 2013 *)
%t LinearRecurrence[{6,-9,4},{1,5,18},30] (* _Harvey P. Dale_, Jun 02 2016 *)
%o (Magma) [4^n+n: n in [0..30]]; // _Vincenzo Librandi_, Jun 16 2013
%o (PARI) a(n)=4^n+n \\ _Charles R Greathouse IV_, Oct 07 2015
%o (Sage) [n+4^n for n in (0..30)] # _G. C. Greubel_, Mar 04 2020
%o (GAP) List([0..30], n-> n+4^n); # _G. C. Greubel_, Mar 04 2020
%Y Cf. A006127, A081552, A104743, A104745.
%K nonn,easy
%O 0,2
%A _Philippe Deléham_, Mar 28 2009
%E Corrected typo in a(22) from _R. J. Mathar_, Mar 29 2009
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