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 A162485 #37 Jun 28 2025 00:59:57
%S A162485 4,6,16,34,84,198,480,1154,2788,6726,16240,39202,94644,228486,551616,
%T A162485 1331714,3215044,7761798,18738640,45239074,109216788,263672646,
%U A162485 636562080,1536796802,3710155684,8957108166,21624372016,52205852194,126036076404,304278004998,734592086400
%N A162485 a(1)=4, a(2)=6; for n > 2, a(n) = 2*a(n-1) + a(n-2) - 4*((n-1) mod 2).
%C A162485 a(n) is the number of perfect matchings of an edge-labeled 2 X n Klein bottle grid graph, or equivalently the number of domino tilings of a 2 X n Klein bottle grid. (The twist is on the length-2 side.)
%H A162485 Paolo Xausa, <a href="/A162485/b162485.txt">Table of n, a(n) for n = 1..1000</a>
%H A162485 Sarah-Marie Belcastro, <a href="https://cs.uwaterloo.ca/journals/JIS/VOL26/Belcastro/belcastro4.html">Domino Tilings of 2 X n Grids (or Perfect Matchings of Grid Graphs) on Surfaces</a>, J. Integer Seq. 26 (2023), Article 23.5.6.
%H A162485 <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (2,2,-2,-1).
%F A162485 For n > 1, a(n) = (1/2)*((1 + sqrt(2))^n*(2 + (-1 + sqrt(2))^(2*floor((1/2)*(-1 + n)))*(-4 + 3*sqrt(2))) + (1 - sqrt(2))^n*(2 - (-1 - sqrt(2))^(2*floor((1/2)*(-1 + n)))*(4 + 3*sqrt(2)))).
%F A162485 From _Colin Barker_, May 01 2012: (Start)
%F A162485 a(n) = 1 - (-1)^n + (1-sqrt(2))^n + (1+sqrt(2))^n.
%F A162485 G.f.: 2*x*(2-x-2*x^2-x^3)/(1-x)/(1+x)/(1-2*x-x^2). (End)
%F A162485 a(n) = A002203(n) + 1 - (-1)^n. - _R. J. Mathar_, Oct 08 2016
%e A162485 a(3) = 2*a(2) + a(1) - 4*(2 mod 2) = 2*6 + 4 - 0 = 16.
%t A162485 LinearRecurrence[{2, 2, -2, -1}, {4, 6, 16, 34}, 50] (* _Paolo Xausa_, Jun 27 2025 *)
%Y A162485 Cf. A002203.
%K A162485 easy,nonn
%O A162485 1,1
%A A162485 _Sarah-Marie Belcastro_, Jul 04 2009