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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

Table of n, a(n) for n=0..25.

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.)