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 A084153 #11 Oct 11 2022 00:50:59
%S A084153 0,0,1,6,33,170,861,4326,21673,108450,542421,2712446,13562913,
%T A084153 67815930,339082381,1695417366,8477097753,42385510610,211927596741,
%U A084153 1059638071086,5298190530193,26490953000490,132454765701501,662273829905606
%N A084153 Binomial transform of a Jacobsthal convolution.
%C A084153 Binomial transform of A084152.
%H A084153 G. C. Greubel, <a href="/A084153/b084153.txt">Table of n, a(n) for n = 0..1000</a>
%H A084153 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (6,-3,-10).
%F A084153 a(n) = (5^n - 2*2^n + (-1)^n)/18.
%F A084153 G.f.: x^2/((1+x)*(1-2*x)*(1-5*x)).
%F A084153 E.g.f.: exp(x)*(exp(2*x) - exp(-x))^2/18 = (exp(5*x) - 2*exp(2*x) + exp(-x))/18.
%t A084153 LinearRecurrence[{6,-3,-10}, {0,0,1}, 41] (* _G. C. Greubel_, Oct 10 2022 *)
%o A084153 (Magma) [(5^n -2^(n+1) +(-1)^n)/18: n in [0..40]]; // _G. C. Greubel_, Oct 10 2022
%o A084153 (SageMath) [(5^n -2^(n+1) +(-1)^n)/18 for n in range(41)] # _G. C. Greubel_, Oct 10 2022
%Y A084153 Cf. A084152.
%K A084153 easy,nonn
%O A084153 0,4
%A A084153 _Paul Barry_, May 16 2003