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 A219867 #18 Aug 31 2024 16:51:10 %S A219867 1,1,4,14,41,143,472,1562,5233,17395,58002,193346,644219,2147421, %T A219867 7156704,23852324,79497767,264952955,883057354,2943113598,9809007073, %U A219867 32692164351,108958689984,363145140266,1210315480391,4033823637937,13444208923518,44807796457932 %N A219867 Number of tilings of a 3 X n rectangle using dominoes and straight (3 X 1) trominoes. %H A219867 Alois P. Heinz, <a href="/A219867/b219867.txt">Table of n, a(n) for n = 0..1000</a> %H A219867 <a href="/index/Rec#order_18">Index entries for linear recurrences with constant coefficients</a>, signature (1,5,12,-3,-11,-30,-5,-13,24,14,24,-3,3,-10,-5,-4,-1,-1). %F A219867 G.f.: see Maple program. %e A219867 a(2) = 4, because there are 4 tilings of a 3 X 2 rectangle using dominoes and straight (3 X 1) trominoes: %e A219867 .___. .___. .___. .___. %e A219867 | | | |___| | | | |___| %e A219867 | | | |___| |_|_| | | | %e A219867 |_|_| |___| |___| |_|_| %p A219867 gf:= -(x^15 +x^13 +x^12 +6*x^11 -x^10 +3*x^9 -10*x^8 -4*x^7 -9*x^6 +2*x^5 +2*x^4 +7*x^3 +2*x^2 -1) / (x^18 +x^17 +4*x^16 +5*x^15 +10*x^14 -3*x^13 +3*x^12 -24*x^11 -14*x^10 -24*x^9 +13*x^8 +5*x^7 +30*x^6 +11*x^5 +3*x^4 -12*x^3 -5*x^2 -x +1): %p A219867 a:= n-> coeff(series(gf, x, n+1), x, n): %p A219867 seq(a(n), n=0..30); %Y A219867 Column k=3 of A219866. %K A219867 nonn,easy %O A219867 0,3 %A A219867 _Alois P. Heinz_, Nov 30 2012