This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A122069 #36 Sep 15 2024 06:50:58
%S A122069 1,3,18,81,405,1944,9477,45927,223074,1082565,5255361,25509168,
%T A122069 123825753,601059771,2917611090,14162371209,68745613437,333698181192,
%U A122069 1619805064509,7862698824255,38166342053346,185263315578333
%N A122069 a(n) = 3*a(n-1) + 9*a(n-2) for n > 1, with a(0)=1, a(1)=3.
%H A122069 G. C. Greubel, <a href="/A122069/b122069.txt">Table of n, a(n) for n = 0..1000</a>
%H A122069 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (3,9).
%F A122069 a(n) = 3^n*Fibonacci(n+1) = 3^n*A000045(n+1).
%F A122069 a(n) = Sum_{k=0..n} 2^k*A016095(n,k).
%F A122069 G.f.: 1/(1-3*x-9*x^2).
%F A122069 Limit_{n->oo} a(n+1)/a(n) = 3*(1+sqrt(5))/2.
%F A122069 a(n) = A099012(n+1). - _R. J. Mathar_, Aug 02 2008
%F A122069 a(n) = A085504(n) for n >= 2. - _Georg Fischer_, Nov 03 2018
%p A122069 with(combinat); seq(3^n*fibonacci(n+1), n=0..25); # _G. C. Greubel_, Oct 03 2019
%t A122069 Table[3^n*Fibonacci[n+1], {n,0,25}] (* _G. C. Greubel_, Oct 03 2019 *)
%t A122069 LinearRecurrence[{3,9},{1,3},30] (* _Harvey P. Dale_, Apr 28 2020 *)
%o A122069 (Sage) [lucas_number1(n,3,-9) for n in range(1, 23)] # _Zerinvary Lajos_, Apr 22 2009
%o A122069 (PARI) vector(26, n, 3^(n-1)*fibonacci(n) ) \\ _G. C. Greubel_, Oct 03 2019
%o A122069 (Magma) [3^n*Fibonacci(n+1): n in [0..25]]; // _G. C. Greubel_, Oct 03 2019
%o A122069 (GAP) List([0..25], n-> 3^n*Fibonacci(n+1) ); # _G. C. Greubel_, Oct 03 2019
%Y A122069 Third row of A234357.
%Y A122069 Cf. A000045, A085504, A099012.
%K A122069 nonn,easy
%O A122069 0,2
%A A122069 _Philippe Deléham_, Oct 15 2006
%E A122069 Corrected by _T. D. Noe_, Nov 07 2006