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 A272144 #55 Sep 08 2022 08:46:16
%S A272144 0,0,1,4,12,30,69,150,316,652,1329,2688,5412,10866,21781,43618,87300,
%T A272144 174672,349425,698940,1397980,2796070,5592261,11184654,22369452,
%U A272144 44739060,89478289,178956760,357913716,715827642,1431655509,2863311258,5726622772
%N A272144 Convolution of A000217 and A001045.
%H A272144 Colin Barker, <a href="/A272144/b272144.txt">Table of n, a(n) for n = 0..1000</a>
%H A272144 <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (4,-4,-2,5,-2).
%F A272144 a(n) = Sum{k=0..n} A000217(k) * A001045(n-k). - _Joerg Arndt_, May 17 2016
%F A272144 a(n) = 4*a(n-1) - 4*a(n-2) - 2*a(n-3) + 5*a(n-4) - 2*a(n-5).
%F A272144 G.f.: x^2/((1-x)^3*(1+x)*(1-2*x)).
%F A272144 a(n+2) = (-105+(-1)^n+2^(7+n)-48*n-6*n^2)/24. - _Colin Barker_, Apr 21 2016
%F A272144 E.g.f.: (exp(-x) + 32*exp(2*x) - 3*(11 + 10*x + 2*x^2)*exp(x))/24. - _Ilya Gutkovskiy_, Apr 21 2016
%e A272144 a(4) = 12 = 0*10+1*6+1*3+3*1+5*0 from A000217: 0,1,3,6,10,... and A001045: 0,1,1,3,5,11,...
%p A272144 seq(coeff(series(x^2/((1-x)^3*(1+x)*(1-2*x)),x,n+1), x, n), n = 0 .. 35); # _Muniru A Asiru_, Oct 26 2018
%t A272144 CoefficientList[Series[x^2/((1 - x)^3 (1 + x) (1 - 2 x)), {x, 0, 30}], x] (* _Michael De Vlieger_, Apr 21 2016 *)
%o A272144 (PARI) concat([0, 0], Vec(x^2/((1-x)^3*(1+x)*(1-2*x)) + O(x^40))) \\ _Altug Alkan_, Apr 21 2016
%o A272144 (Magma) m:=40; R<x>:=PowerSeriesRing(Integers(), m); [0,0] cat Coefficients(R!(x^2/((1-x)^3*(1+x)*(1-2*x)))); // _G. C. Greubel_, Oct 26 2018
%Y A272144 Partial Sums of A011377(n-2)=A178420(n-1).
%K A272144 nonn,easy
%O A272144 0,4
%A A272144 _Patrick Okolo Edeogu_, Apr 21 2016