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.

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

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