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 A368529 #23 Jan 29 2024 06:14:48
%S A368529 0,1,8,41,180,745,3016,12113,48516,194145,776680,3106841,12427508,
%T A368529 49710201,198841000,795364225,3181457156,12725828913,50903315976,
%U A368529 203613264265,814453057460,3257812230281,13031248921608,52124995686961,208499982748420,833999930994305
%N A368529 a(n) = Sum_{k=1..n} k^2 * 4^(n-k).
%H A368529 Paolo Xausa, <a href="/A368529/b368529.txt">Table of n, a(n) for n = 0..1000</a>
%H A368529 <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (7,-15,13,-4).
%F A368529 G.f.: x * (1+x)/((1-4*x) * (1-x)^3).
%F A368529 a(n) = 7*a(n-1) - 15*a(n-2) + 13*a(n-3) - 4*a(n-4).
%F A368529 a(n) = A052161(n-1) + A052161(n-2) for n > 1.
%F A368529 a(n) = (5*4^(n+1) - (9*n^2 + 24*n + 20))/27.
%F A368529 a(0) = 0; a(n) = 4*a(n-1) + n^2.
%t A368529 LinearRecurrence[{7, -15, 13, -4}, {0, 1, 8, 41}, 30] (* _Paolo Xausa_, Jan 29 2024 *)
%o A368529 (PARI) a(n) = sum(k=1, n, k^2*4^(n-k));
%Y A368529 Cf. A000290, A000330, A047520, A368528.
%Y A368529 Cf. A052161, A368524.
%Y A368529 Cf. A014825, A368530.
%K A368529 nonn,easy
%O A368529 0,3
%A A368529 _Seiichi Manyama_, Dec 28 2023