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A318268 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 3 such pairs are joined by an edge. 8
0, 0, 0, 2, 34, 250, 1234, 4830, 16174, 48444, 133416, 344220, 843020, 1978804, 4484228, 9865742, 21166390, 44439910, 91570126, 185614242, 370846914, 731502296, 1426514540, 2753525208, 5266164280, 9987859912, 18799814312, 35141997050, 65274659562, 120540177522 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,4
COMMENTS
This is also the number of "(n-3)-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 (7,-17,11,19,-29,-3,21,-3,-7,1,1).
FORMULA
G.f.: x^2*(2*x + 20*x^2 + 46*x^3 + 40*x^4 + 30*x^5 + 4*x^6 + 4*x^7)/(1 - x)^3/(1 - x - x^2)^4 (conjectured).
The above conjecture is true. The PARI program given in the links can be used to establish an upper limit on the order of the linear recurrence and sufficient number of terms to prove correctness. - Andrew Howroyd, Sep 03 2018
EXAMPLE
See example in A318267.
MATHEMATICA
CoefficientList[Normal[Series[x^2(2*x + 20*x^2 + 46*x^3 + 40*x^4 + 30*x^5 + 4*x^6 + 4*x^7)/(1 - x)^3/(1 - x - x^2)^4, {x, 0, 30}]], x]
LinearRecurrence[{7, -17, 11, 19, -29, -3, 21, -3, -7, 1, 1}, {0, 0, 0, 2, 34, 250, 1234, 4830, 16174, 48444, 133416}, 30] (* Harvey P. Dale, Aug 05 2019 *)
CROSSREFS
Sequence in context: A064202 A206624 A131471 * A036827 A136362 A220507
KEYWORD
nonn,easy
AUTHOR
Donovan Young, Aug 22 2018
EXTENSIONS
Terms a(14) and beyond from Andrew Howroyd, Sep 03 2018
STATUS
approved

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Last modified May 21 13:22 EDT 2024. Contains 372736 sequences. (Running on oeis4.)