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A318268
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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.
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8
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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
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OFFSET
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0,4
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COMMENTS
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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
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LINKS
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Index entries for linear recurrences with constant coefficients, signature (7,-17,11,19,-29,-3,21,-3,-7,1,1).
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FORMULA
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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
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EXAMPLE
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MATHEMATICA
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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 *)
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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