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A318269 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. 7
0, 0, 0, 0, 21, 347, 2919, 17050, 78815, 309075, 1072617, 3386970, 9921030, 27338000, 71614370, 179788174, 435311905, 1021684125, 2333955085, 5207067714, 11377225161, 24403026561, 51484962205, 107024887620, 219528748908, 444886466640, 891735024852, 1769575953980 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,5

COMMENTS

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

LINKS

Table of n, a(n) for n=0..27.

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 (9,-31,44,4,-84,66,46,-74,-4,36,-4,-9,1,1).

FORMULA

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).

The above conjecture is true. See A318268. - Andrew Howroyd, Sep 03 2018

EXAMPLE

See example in A318267.

MATHEMATICA

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]

CROSSREFS

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

Sequence in context: A323277 A075921 A201878 * A298229 A298153 A299127

Adjacent sequences:  A318266 A318267 A318268 * A318270 A318271 A318272

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 20 07:21 EDT 2020. Contains 337264 sequences. (Running on oeis4.)