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 A316726 #26 Jul 17 2025 00:38:39
%S A316726 2,4,15,46,150,480,1545,4964,15958,51292,164871,529946,1703418,
%T A316726 5475328,17599457,56570280,181834970,584475732,1878691887,6038716422,
%U A316726 19410365422,62391120800,200545011401,644615789580,2072001259342,6660074556204,21407609138375
%N A316726 The number of ways to tile (with squares and rectangles) a 2 X (n+2) strip with the upper left and upper right squares removed.
%C A316726 Each number in the sequence is the partial sum of A033505 (n starts at 0, each number add one if n is even). We can also find the recursion relation a(n) = 2*a(n-1) + 4*a(n-2) - a(n-4) for the sequence, which can be proved by induction.
%H A316726 Colin Barker, <a href="/A316726/b316726.txt">Table of n, a(n) for n = 0..1000</a>
%H A316726 <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (2,4,0,-1).
%F A316726 a(n) = 2*a(n-1) + 4*a(n-2) - a(n-4) for n>=4.
%F A316726 G.f.: (2 - x^2) / ((1 + x)*(1 - 3*x - x^2 + x^3)). - _Colin Barker_, Jul 12 2018
%F A316726 a(n) = A030186(n) + 2*A033505(n-1) + a(n-2). - _Greg Dresden_ and Ge Ma, Jul 12 2025
%e A316726 For n=4, a(4) = 150 = 2*a(3) + 4*a(2) - a(0).
%t A316726 CoefficientList[ Series[(-x^2 + 1)/(x^4 - 4x^2 - 2x + 1), {x, 0, 27}], x] (* or *) LinearRecurrence[{2, 4, 0, -1}, {2, 4, 15, 46}, 27] (* _Robert G. Wilson v_, Jul 15 2018 *)
%o A316726 (PARI) Vec((2 - x^2) / ((1 + x)*(1 - 3*x - x^2 + x^3)) + O(x^30)) \\ _Colin Barker_, Jul 12 2018
%Y A316726 Cf. A033505, A030186.
%K A316726 nonn,easy
%O A316726 0,1
%A A316726 _Zijing Wu_, Jul 11 2018
%E A316726 More terms from _Colin Barker_, Jul 12 2018