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 A123520 #19 Oct 15 2017 01:00:01
%S A123520 4,28,152,744,3436,15284,66224,281424,1178196,4874444,19973192,
%T A123520 81189688,327817404,1316035940,5257118560,20909651104,82849544868,
%U A123520 327163551612,1288036695544,5057236343176,19807689093644,77408388584724
%N A123520 Number of vertical dominoes in all possible tilings of a 2n X 3 grid by dominoes.
%H A123520 G. C. Greubel, <a href="/A123520/b123520.txt">Table of n, a(n) for n = 1..1000</a> (terms 0..100 from Vincenzo Librandi)
%H A123520 <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (8,-18,8,-1).
%F A123520 a(n) = Sum_{k=0..n} 2^(k+1) * k * C(n+k,2*k).
%F A123520 a(n) = Sum_{k=0..n} k * A123519(n,k).
%F A123520 G.f.: 4*z*(1-z)/(1-4*z+z^2)^2.
%F A123520 a(n) = (2+sqrt(3))^n*((1+sqrt(3))*n+1/sqrt(3))/3 + (2-sqrt(3))^n*((1-sqrt(3))*n-1/sqrt(3))/3. - _Vaclav Kotesovec_, Nov 29 2012
%e A123520 a(1) = 4 because a 2 X 3 grid can be tiled in 3 ways with dominoes: 3 horizontal dominoes, 1 horizontal domino above two adjacent vertical dominoes and 1 horizontal domino below two adjacent vertical dominoes; these have altogether 4 vertical dominoes.
%p A123520 a:=n->sum(k*2^(k+1)*binomial(n+k,2*k),k=0..n): seq(a(n),n=1..24);
%t A123520 FullSimplify[Table[(2+Sqrt[3])^n*((1+Sqrt[3])*n+1/Sqrt[3])/3 + (2-Sqrt[3])^n*((1-Sqrt[3])*n-1/Sqrt[3])/3,{n,1,20}]] (* _Vaclav Kotesovec_, Nov 29 2012 *)
%t A123520 Table[Sum[2^(k + 1)*k*Binomial[n + k, 2 k], {k, 0, n}], {n, 0, 50}] (* _G. C. Greubel_, Oct 14 2017 *)
%o A123520 (PARI) z='z+O('z^50); Vec(4*z*(1-z)/(1-4*z+z^2)^2) \\ _G. C. Greubel_, Oct 14 2017
%Y A123520 Cf. A001835, A123519.
%K A123520 nonn,easy
%O A123520 1,1
%A A123520 _Emeric Deutsch_, Oct 16 2006