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 A318268 #43 Mar 20 2020 15:08:56
%S A318268 0,0,0,2,34,250,1234,4830,16174,48444,133416,344220,843020,1978804,
%T A318268 4484228,9865742,21166390,44439910,91570126,185614242,370846914,
%U A318268 731502296,1426514540,2753525208,5266164280,9987859912,18799814312,35141997050,65274659562,120540177522
%N A318268 a(n) is the number of configurations of n indistinguishable pairs placed on the vertices of the ladder graph P_2 X P_n such that all but 3 such pairs are joined by an edge.
%C A318268 This is also the number of "(n-3)-domino" configurations in the game of memory played on a 2 X n rectangular array, see [Young]. - _Donovan Young_, Oct 23 2018
%H A318268 Andrew Howroyd, <a href="/A318268/a318268.txt">PARI program based on combinatorial definition</a>
%H A318268 D. Young, <a href="https://cs.uwaterloo.ca/journals/JIS/VOL21/Young/young2.html">The Number of Domino Matchings in the Game of Memory</a>, Journal of Integer Sequences, Vol. 21 (2018), Article 18.8.1.
%H A318268 Donovan Young, <a href="https://arxiv.org/abs/1905.13165">Generating Functions for Domino Matchings in the 2 * k Game of Memory</a>, arXiv:1905.13165 [math.CO], 2019. Also in <a href="https://www.emis.de/journals/JIS/VOL22/Young/young13.html">J. Int. Seq.</a>, Vol. 22 (2019), Article 19.8.7.
%H A318268 <a href="/index/Rec#order_11">Index entries for linear recurrences with constant coefficients</a>, signature (7,-17,11,19,-29,-3,21,-3,-7,1,1).
%F A318268 G.f.: x^2*(2*x + 20*x^2 + 46*x^3 + 40*x^4 + 30*x^5 + 4*x^6 + 4*x^7)/(1 - x)^3/(1 - x - x^2)^4 (conjectured).
%F A318268 The above conjecture is true. The PARI program given in the links can be used to establish an upper limit on the order of the linear recurrence and sufficient number of terms to prove correctness. - _Andrew Howroyd_, Sep 03 2018
%e A318268 See example in A318267.
%t A318268 CoefficientList[Normal[Series[x^2(2*x + 20*x^2 + 46*x^3 + 40*x^4 + 30*x^5 + 4*x^6 + 4*x^7)/(1 - x)^3/(1 - x - x^2)^4, {x, 0, 30}]], x]
%t A318268 LinearRecurrence[{7,-17,11,19,-29,-3,21,-3,-7,1,1},{0,0,0,2,34,250,1234,4830,16174,48444,133416},30] (* _Harvey P. Dale_, Aug 05 2019 *)
%Y A318268 Cf. A046741, A318243, A318244, A318267, A318269, A318270.
%K A318268 nonn,easy
%O A318268 0,4
%A A318268 _Donovan Young_, Aug 22 2018
%E A318268 Terms a(14) and beyond from _Andrew Howroyd_, Sep 03 2018