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A254126
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The number of tilings of a 5 X n rectangle using integer length rectangles with at least one length of size 1, i.e., tiles are 1 X 1, 1 X 2, ..., 1 X n, 2 X 1, 3 X 1, 4 X 1, 5 X 1.
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7
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1, 16, 533, 22873, 1064576, 50796983, 2441987149, 117656540512, 5672528575545, 273541357254277, 13191518965300160, 636171495829068099, 30680036092304563369, 1479579136691648516016, 71354395560692698401005, 3441147782121276015384833, 165953315828852845775456128
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OFFSET
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0,2
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COMMENTS
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Let G_n be the graph with vertices {(a,b) : 1<=a<=9, 1<=b<=2n-1, a+b odd} and edges between (a,b) and (c,d) if and only if |a-b|=|c-d|=1. Then a(n) is the number of independent sets in G_n.
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LINKS
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FORMULA
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G.f: (1 - 58*x + 799*x^2 - 4041*x^3 + 8286*x^4 - 7357*x^5 + 2660*x^6 - 312*x^7)/(1 - 74*x + 1450*x^2 - 10672*x^3 + 34214*x^4 - 50814*x^5 + 34671*x^6 - 9772*x^7 + 936*x^8).
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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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STATUS
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approved
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