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 A356622 #11 Aug 17 2022 22:39:50
%S A356622 1,5,39,317,2585,21085,171987,1402873,11443033,93339173,761354199,
%T A356622 6210256613,50656169297,413195081581,3370372805763,27491645850097,
%U A356622 224245398092113,1829137434684101,14920010771362215
%N A356622 Number of ways to tile a hexagonal strip made up of 4*n equilateral triangles, using triangles and diamonds.
%C A356622 Here is the hexagonal strip:
%C A356622 ________________ ____
%C A356622 /\ /\ /\ /\ / \ /
%C A356622 /__\/__\/__\/__\/ ... \/
%C A356622 \ /\ /\ /\ /\ /\
%C A356622 \/__\/__\/__\/__\ /__\
%C A356622 The two types of tiles are triangles and diamonds (each of which can be rotated). Here are the two types of tiles:
%C A356622 ____ ____
%C A356622 \ / \ \
%C A356622 \/ and \___\.
%H A356622 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (9,-7,1).
%F A356622 a(n) = A355327(2*n).
%F A356622 a(n) = 9*a(n-1) - 7*a(n-2) + a(n-3).
%F A356622 G.f.: (1 - 4 x + x^2)/(1 - 9 x + 7 x^2 - x^3).
%e A356622 For n=4, here is one of the a(4)=2585 ways to tile this strip (of 16 triangles) using triangles and diamonds.
%e A356622 ________________
%e A356622 / /\ /\ / /
%e A356622 /__ / \/__\/__ /
%e A356622 \ /\ /\ \ /\
%e A356622 \/__\/__\___\/__\
%t A356622 LinearRecurrence[{9, -7, 1}, {1, 5, 39}, 40]
%Y A356622 Bisection of A355327. Cf. A356623.
%K A356622 nonn,easy
%O A356622 0,2
%A A356622 _Greg Dresden_ and _Aarnav Gogri_, Aug 16 2022