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

Author

Donovan Young, Aug 23 2018

Keywords

• nonn
• easy

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

Examples

			See example in A318267.
		

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).

Crossrefs

Cf. A046741, A318243, A318244, A318267, A318268, A318269.

Programs

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]

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

Extensions

Terms a(14) and beyond from Andrew Howroyd, Sep 03 2018