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A364587
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Clique covering number, independence number, and Shannon capacity of the n-Lucas cube graph.
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0
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1, 2, 3, 4, 6, 10, 15, 24, 39, 62, 100, 162, 261, 422, 683, 1104, 1786, 2890, 4675, 7564, 12239, 19802, 32040, 51842, 83881, 135722, 219603, 355324, 574926, 930250, 1505175, 2435424, 3940599, 6376022, 10316620, 16692642, 27009261, 43701902, 70711163, 114413064
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OFFSET
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1,2
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COMMENTS
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For n > 1, also the edge cover number and number of edge cuts in the n-Lucas cube graph. - Eric W. Weisstein, Aug 03 2023
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LINKS
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E. Munarini, C. Perelli Cippo, and N. Zagaglia Salvi, On the Lucas Cubes, Fibonacci Quart. 39 (2001), 12-21.
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FORMULA
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a(n) = (4 + 3*LucasL[n] + 2*cos(2*n*Pi/3))/6.
a(n) = a(n-1) + a(n-2) + a(n-3) - a(n-4) - a(n-5).
G.f.: x*(1+x-2*x^3-2*x^4)/(1-x-x^2-x^3+x^4+x^5).
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MATHEMATICA
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Table[(4 + 3 LucasL[n] + 2 Cos[2 n Pi/3])/6, {n, 20}]
LinearRecurrence[{1, 1, 1, -1, -1}, {1, 2, 3, 4, 6}, 20]
CoefficientList[Series[(1 + x - 2 x^3 - 2 x^4)/(1 - x - x^2 - x^3 + x^4 + x^5), {x, 0, 20}], x]
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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