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 A368528 #13 Dec 29 2023 08:05:14
%S A368528 0,1,7,30,106,343,1065,3244,9796,29469,88507,265642,797070,2391379,
%T A368528 7174333,21523224,64569928,193710073,581130543,1743391990,5230176370,
%U A368528 15690529551,47071589137,141214767940,423644304396,1270932913813,3812798742115
%N A368528 a(n) = Sum_{k=1..n} k^2 * 3^(n-k).
%H A368528 <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (6,-12,10,-3).
%F A368528 G.f.: x * (1+x)/((1-3*x) * (1-x)^3).
%F A368528 a(n) = 6*a(n-1) - 12*a(n-2) + 10*a(n-3) - 3*a(n-4).
%F A368528 a(n) = A052150(n-1) + A052150(n-2) for n > 1.
%F A368528 a(n) = (3^(n+1) - (n^2 + 3*n + 3))/2.
%F A368528 a(0) = 0; a(n) = 3*a(n-1) + n^2.
%o A368528 (PARI) a(n) = sum(k=1, n, k^2*3^(n-k));
%Y A368528 Cf. A000290, A000330, A047520, A368529.
%Y A368528 Cf. A052150, A368524.
%K A368528 nonn,easy
%O A368528 0,3
%A A368528 _Seiichi Manyama_, Dec 28 2023