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 A106517 #27 Sep 08 2022 08:45:18
%S A106517 1,3,10,31,95,288,869,2615,7858,23595,70819,212512,637625,1913019,
%T A106517 5739290,17218247,51655351,154967040,464902717,1394710735,4184136386,
%U A106517 12552415923,37657258715,112971793856,338915410225,1016746277043
%N A106517 Convolution of Fibonacci(n-1) and 3^n.
%H A106517 G. C. Greubel, <a href="/A106517/b106517.txt">Table of n, a(n) for n = 0..1000</a>
%H A106517 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (4,-2,-3).
%F A106517 G.f.: (1-x)/((1-x-x^2)*(1-3*x)).
%F A106517 a(n) = Sum_{k=0..n} Fibonacci(n-k-1) * 3^k.
%F A106517 a(n) = A101220(2, 3, n+1). - _Ross La Haye_, Jul 25 2005
%F A106517 a(n) = A101220(3, 3, n+1) - A101220(3, 3, n). - _Ross La Haye_, May 31 2006
%F A106517 a(n) = (1/5)*(6*3^n - Lucas(n+1)). - _Ralf Stephan_, Nov 16 2010
%F A106517 Sum_{k=0..n} a(k) = A094688(n+1). - _G. C. Greubel_, Aug 05 2021
%t A106517 LinearRecurrence[{4,-2,-3},{1,3,10},30] (* _Harvey P. Dale_, Oct 08 2014 *)
%o A106517 (Magma) I:=[1,3,10]; [n le 3 select I[n] else 4*Self(n-1) -2*Self(n-2) -3*Self(n-3): n in [1..41]]; // _G. C. Greubel_, Aug 05 2021
%o A106517 (Sage) [(2*3^(n+1) - lucas_number2(n+1, 1, -1))/5 for n in (0..40)] # _G. C. Greubel_, Aug 05 2021
%o A106517 (PARI) a(n) = sum(k=0, n, fibonacci(n-k-1) * 3^k); \\ _Michel Marcus_, Aug 06 2021
%Y A106517 Cf. A000032, A000045, A000244, A094688, A101220.
%Y A106517 Diagonal sums of number triangle A106516.
%K A106517 easy,nonn
%O A106517 0,2
%A A106517 _Paul Barry_, May 05 2005