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 A123194 #18 Sep 08 2022 08:45:28
%S A123194 4,7,12,23,43,81,150,275,498,893,1587,2799,4904,8543,14808,25555,
%T A123194 43931,75261,128538,218923,371934,630457,1066467,1800603,3034828,
%U A123194 5106871,8580900,14398415,24129163,40388073,67527582,112786499,188195274,313733813,522562323
%N A123194 a(n) = (n+1)*Fibonacci(n+2) + 3.
%H A123194 Vincenzo Librandi, <a href="/A123194/b123194.txt">Table of n, a(n) for n = 0..1000</a>
%H A123194 Philip Matchett Wood, <a href="http://www.emis.de/journals/INTEGERS/papers/g2/g2.Abstract.html">A bijective proof of f_{n+4}+f_1+2f_2+...+nf_n=(n+1)f_{n+2}+3</a>, Integers 6 (2006), A2, 4 pp.
%H A123194 <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (3,-1,-3,1,1).
%F A123194 G.f.: (4 - 5*x - 5*x^2 + 6*x^3 + 3*x^4)/((1 - x)*(1 - x - x^2)^2). - _Ilya Gutkovskiy_, Feb 24 2017
%F A123194 From _Colin Barker_, Feb 25 2017: (Start)
%F A123194 a(n) = 3 - 2^(-1-n)*((1-sqrt(5))^n*(-5+3*sqrt(5)) - (1+sqrt(5))^n*(5+3*sqrt(5)))/5*(1+n).
%F A123194 a(n) = 3*a(n-1) - a(n-2) - 3*a(n-3) + a(n-4) + a(n-5) for n>4.
%F A123194 (End)
%t A123194 Table[(n + 1) Fibonacci[n+2] + 3, {n, 0, 40}] (* _Vincenzo Librandi_, Feb 25 2017 *)
%t A123194 LinearRecurrence[{3,-1,-3,1,1},{4,7,12,23,43},40] (* _Harvey P. Dale_, Jan 12 2018 *)
%o A123194 (PARI) a(n) = (n+1)*fibonacci(n+2) + 3; \\ _Michel Marcus_, Feb 25 2017
%o A123194 (PARI) Vec((4 - 5*x - 5*x^2 + 6*x^3 + 3*x^4)/((1 - x)*(1 - x - x^2)^2) + O(x^50)) \\ _Colin Barker_, Feb 25 2017
%o A123194 (Magma) [(n+1)*Fibonacci(n+2) + 3: n in [0..40]]; // _Vincenzo Librandi_, Feb 25 2017
%Y A123194 Cf. A023607.
%K A123194 nonn
%O A123194 0,1
%A A123194 _N. J. A. Sloane_, Oct 04 2006