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 A131412 #13 Sep 08 2022 08:45:31
%S A131412 1,2,7,15,32,62,117,214,385,683,1200,2092,3625,6250,10731,18359,31312,
%T A131412 53258,90365,152990,258501,435987,734112,1234200,2072017,3474002,
%U A131412 5817487,9730719,16258880,27139478,45258885,75408742,125538505,208828475,347119056,576580804
%N A131412 a(n) = n*(Fibonacci(n) - 1) + Fibonacci(n + 2) - 1.
%H A131412 Andrew Howroyd, <a href="/A131412/b131412.txt">Table of n, a(n) for n = 1..1000</a>
%H A131412 <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (4,-4,-2,4,0,-1).
%F A131412 From _Andrew Howroyd_, Aug 10 2018: (Start)
%F A131412 a(n) = n*(Fibonacci(n) - 1) + Sum_{k=1..n} Fibonacci(k).
%F A131412 a(n) = 4*a(n-1) - 4*a(n-2) - 2*a(n-3) + 4*a(n-4) - a(n-6).
%F A131412 G.f.: x*(1 - 2*x + 3*x^2 - 3*x^3)/((1 - x)^2*(1 - x - x^2)^2).
%F A131412 (End)
%e A131412 a(4) = 15 = sum of row 4, triangle A131411; (3 + 3 + 4 + 5).
%t A131412 With[{F=Fibonacci}, Table[F[n+2]+n*F[n]-(n+1), {n,40}]] (* _G. C. Greubel_, Jul 13 2019 *)
%o A131412 (PARI) a(n) = n*(fibonacci(n) - 1) + fibonacci(n+2) - 1; \\ _Andrew Howroyd_, Aug 10 2018
%o A131412 (PARI) Vec((1 - 2*x + 3*x^2 - 3*x^3)/((1 - x)^2*(1 - x - x^2)^2) + O(x^40)) \\ _Andrew Howroyd_, Aug 10 2018
%o A131412 (Magma) F:=Fibonacci; [F(n+2)+n*F(n)-(n+1): n in [1..40]]; // _G. C. Greubel_, Jul 13 2019
%o A131412 (Sage) f=fibonacci; [f(n+2)+n*f(n)-(n+1) for n in (1..40)] # _G. C. Greubel_, Jul 13 2019
%o A131412 (GAP) F:=Fibonacci;; List([1..40], n-> F(n+2)+n*F(n)-(n+1)); # _G. C. Greubel_, Jul 13 2019
%Y A131412 Row sums of A131411.
%Y A131412 Cf. A000045, A131253.
%K A131412 nonn
%O A131412 1,2
%A A131412 _Gary W. Adamson_, Jul 08 2007
%E A131412 Name changed and terms a(11) and beyond from _Andrew Howroyd_, Aug 10 2018