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 A376031 #16 Sep 23 2024 07:41:59
%S A376031 1,3,18,112,692,4294,26624,165086,1023662,6347440,39358774,244053158,
%T A376031 1513307844,9383614226,58185263358,360791140032,2237168644134,
%U A376031 13872079956206,86017029971684,533368425534858,3307273890427894,20507514248408832,127161570097317790
%N A376031 Number of ways to tile a 3 x (2*n) rectangle with dominoes and T's.
%C A376031 a(n) is the number of ways to tile a 3 X (2*n) rectangle with two kinds of tiles: dominoes (made up of 2 cells) and T's (made up of 4 cells), each of which can be rotated as needed.
%H A376031 Paolo Xausa, <a href="/A376031/b376031.txt">Table of n, a(n) for n = 0..1000</a>
%H A376031 <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (5,7,4,-8,2).
%F A376031 a(n) = 5*a(n-1) + 7*a(n-2) + 4*a(n-3) - 8*a(n-4) + 2*a(n-5).
%F A376031 G.f.: -(2*x^4-3*x^3-4*x^2-2*x+1)/(2*x^5-8*x^4+4*x^3+7*x^2+5*x-1).
%e A376031 For n=3, here is one of the a(3) = 112 ways to tile a 3 x 6 rectangle using our dominoes and T's:
%e A376031 ___________
%e A376031 | |___| | | |
%e A376031 | _|_ |_|_|
%e A376031 |_|___|_|___|.
%t A376031 LinearRecurrence[{5, 7, 4, -8, 2}, {1, 3, 18, 112, 692}, 30] (* _Paolo Xausa_, Sep 23 2024 *)
%Y A376031 Cf. A033506, A219968, A337492, A346054.
%K A376031 nonn,easy
%O A376031 0,2
%A A376031 _Greg Dresden_ and Lucas MingQu Xia, Sep 06 2024