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 A318270 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 5 such pairs are joined by an edge. 7
 0, 0, 0, 0, 0, 186, 3666, 36714, 253386, 1369260, 6209700, 24668742, 88338174, 290968686, 894709790, 2597386330, 7181246394, 19040425628, 48684375292, 120592523460, 290476059204, 682548818802, 1568744083242, 3534725236308, 7823387477220, 17037467831748 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,6 COMMENTS This is also the number of "(n-5)-domino" configurations in the game of memory played on a 2 X n rectangular array, see [Young]. - Donovan Young, Oct 23 2018 LINKS D. Young, The Number of Domino Matchings in the Game of Memory, Journal of Integer Sequences, Vol. 21 (2018), Article 18.8.1. Donovan Young, Generating Functions for Domino Matchings in the 2 * k Game of Memory, arXiv:1905.13165 [math.CO], 2019. Also in J. Int. Seq., Vol. 22 (2019), Article 19.8.7. Index entries for linear recurrences with constant coefficients, signature (11,-49,105,-75,-123,278,-82,-250,210,90,-150,-5,55,-5,-11,1,1). FORMULA G.f.: x^2*(6*x^13 + 20*x^12 + 228*x^11 + 888*x^10 + 3012*x^9 + 6612*x^8 + 10020*x^7 + 9636*x^6 + 5502*x^5 + 1620*x^4 + 186*x^3)/(1 - x)^5/(1 - x - x^2)^6 (conjectured). The above conjecture is true. See A318268. - Andrew Howroyd, Sep 03 2018 EXAMPLE See example in A318267. MATHEMATICA CoefficientList[Normal[Series[x^2(6*x^13+20*x^12+228*x^11+888*x^10+3012*x^9+6612*x^8+10020*x^7+9636*x^6+5502*x^5+1620*x^4+186*x^3)/(1-x)^5/(1-x-x^2)^6, {x, 0, 30}]], x] CROSSREFS Cf. A046741, A318243, A318244, A318267, A318268, A318269. Sequence in context: A251492 A289301 A147817 * A230898 A241942 A161619 Adjacent sequences:  A318267 A318268 A318269 * A318271 A318272 A318273 KEYWORD nonn,easy AUTHOR Donovan Young, Aug 23 2018 EXTENSIONS Terms a(14) and beyond from Andrew Howroyd, Sep 03 2018 STATUS approved

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Last modified September 25 18:58 EDT 2020. Contains 337344 sequences. (Running on oeis4.)