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 A251701 #22 Dec 03 2024 15:10:55
%S A251701 1,4,13,36,97,268,765,2236,6625,19764,59149,177268,531585,1594492,
%T A251701 4783165,14349132,43046977,129140452,387420813,1162261828,3486784801,
%U A251701 10460353644,31381060093,94143179356,282429537057,847288610068,2541865829005,7625597485716
%N A251701 a(n) = 3^n + n^2.
%H A251701 <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (6,-12,10,-3).
%F A251701 G.f.: (1-2*x+x^2-4*x^3)/((1-3*x)*(1-x)^3).
%F A251701 a(n) = 6*a(n-1)-12*a(n-2)+10*a(n-3)-3*a(n-4) for n>3.
%F A251701 a(n) = A000244(n) + A000290(n).
%p A251701 A251701:=n->3^n + n^2: seq(A251701(n), n=0..40); # _Wesley Ivan Hurt_, Jan 22 2017
%t A251701 Table[3^n + n^2, {n, 0, 40}] (* or *) CoefficientList[Series[(1 - 2 x + x^2 - 4 x^3) / ((1 - 3 x) (1 - x)^3), {x, 0, 40}], x]
%t A251701 LinearRecurrence[{6,-12,10,-3},{1,4,13,36},30] (* _Harvey P. Dale_, Aug 08 2017 *)
%o A251701 (Magma) [3^n+n^2: n in [0..30]];
%o A251701 (Magma) I:=[1,4,13,36]; [n le 4 select I[n] else 6*Self(n-1)-12*Self(n-2)+10*Self(n-3)-3*Self(n-4): n in [1..30]];
%Y A251701 Cf. A000244, A000290, A001585, A104743.
%K A251701 nonn,easy
%O A251701 0,2
%A A251701 _Vincenzo Librandi_, Dec 07 2014