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A318269
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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 4 such pairs are joined by an edge.
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7
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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
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OFFSET
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0,5
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COMMENTS
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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
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LINKS
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Index entries for linear recurrences with constant coefficients, signature (9,-31,44,4,-84,66,46,-74,-4,36,-4,-9,1,1).
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FORMULA
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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).
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EXAMPLE
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MATHEMATICA
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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]
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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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