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 A349842 #10 Dec 21 2021 06:39:28
%S A349842 1,1,2,4,8,17,33,66,132,264,529,1057,2114,4228,8456,16913,33825,67650,
%T A349842 135300,270600,541201,1082401,2164802,4329604,8659208,17318417,
%U A349842 34636833,69273666,138547332,277094664,554189329,1108378657,2216757314,4433514628,8867029256,17734058513
%N A349842 Expansion of 1/((1 - 2*x)*(1 + x + x^2 + x^3 + x^4)).
%C A349842 Number of ways to tile an n-board (an n X 1 array of 1 X 1 cells) using squares, dominoes, trominoes, tetrominoes, black pentominoes, and white pentominoes.
%C A349842 Row sums of A349841.
%H A349842 <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (1,1,1,1,2).
%F A349842 a(n) = a(n-1) + a(n-2) + a(n-3) + a(n-4) + 2*a(n-5) + delta(n,0), a(n<0)=0.
%F A349842 a(n) = 2*a(n-1) + a(n-5) - 2*a(n-6) + delta(n,0) - delta(n,1), a(n<0)=0.
%F A349842 G.f.: 1/(1-x-x^2-x^3-x^4-2*x^5).
%t A349842 CoefficientList[Series[(1 - x)/((1 - x^5)(1 - 2x)), {x, 0, 35}], x]
%Y A349842 Row sums of triangles in the same family as A349841: A000079, A001045, A077947, A115451.
%K A349842 nonn,easy
%O A349842 0,3
%A A349842 _Michael A. Allen_, Dec 13 2021