A318269 - OEIS

%I #40 Mar 20 2020 15:09:04

%S 0,0,0,0,21,347,2919,17050,78815,309075,1072617,3386970,9921030,

%T 27338000,71614370,179788174,435311905,1021684125,2333955085,

%U 5207067714,11377225161,24403026561,51484962205,107024887620,219528748908,444886466640,891735024852,1769575953980

%N 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 4 such pairs are joined by an edge.

%C This is also the number of "(n-4)-domino" configurations in the game of memory played on a 2 X n rectangular array, see [Young]. - _Donovan Young_, Oct 23 2018

%H D. Young, <a href="http://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 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 <a href="/index/Rec#order_14">Index entries for linear recurrences with constant coefficients</a>, signature (9,-31,44,4,-84,66,46,-74,-4,36,-4,-9,1,1).

%F G.f.: x^2*(5*x^10 + 10*x^9 + 93*x^8 + 230*x^7 + 502*x^6 + 612*x^5 + 447*x^4 + 158*x^3 + 21*x^2)/(1 - x)^4/(1 - x - x^2)^5 (conjectured).

%F The above conjecture is true. See A318268. - _Andrew Howroyd_, Sep 03 2018

%e See example in A318267.

%t CoefficientList[Normal[Series[x^2(5*x^10 + 10*x^9 + 93*x^8 + 230*x^7 + 502*x^6 + 612*x^5 + 447*x^4 + 158*x^3 + 21*x^2)/(1 - x)^4/(1 - x - x^2)^5, {x, 0, 30}]], x]

%Y Cf. A046741, A318243, A318244, A318267, A318268, A318270.

%K nonn,easy

%O 0,5

%A _Donovan Young_, Aug 23 2018

%E Terms a(14) and beyond from _Andrew Howroyd_, Sep 03 2018