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A347553
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Number of minimum dominating sets in the n-cycle complement graph.
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1
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1, 4, 5, 9, 14, 20, 27, 35, 44, 54, 65, 77, 90, 104, 119, 135, 152, 170, 189, 209, 230, 252, 275, 299, 324, 350, 377, 405, 434, 464, 495, 527, 560, 594, 629, 665, 702, 740, 779, 819, 860, 902, 945, 989, 1034, 1080, 1127, 1175, 1224, 1274, 1325, 1377, 1430
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OFFSET
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3,2
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LINKS
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Table of n, a(n) for n=3..55.
John Konvalina, On the number of combinations without unit separation, Journal of Combinatorial Theory, Series A 31.2 (1981): 101-107. See Table II, row k=2.
Eric Weisstein's World of Mathematics, Cycle Complement Graph
Eric Weisstein's World of Mathematics, Minimum Dominating Set
Index entries for linear recurrences with constant coefficients, signature (3,-3,1).
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FORMULA
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a(n) = n*(n - 3)/2 for n > 4.
G.f.: x^3*(-1 - x + 4*x^2 - 5*x^3 + 2*x^4)/(-1 + x)^3.
From Stefano Spezia, Sep 08 2021: (Start)
E.g.f.: x*(12 + 6*exp(x)*(x - 2) + 6*x + 2*x^2 + x^3)/12.
a(n) = 3*a(n-1) - 3*a(n-3) + a(n-3) for n > 4. (End)
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MATHEMATICA
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Join[{1, 4}, Table[n(n-3)/2, {n, 5, 20}]]
CoefficientList[Series[x^3(-1 - x + 4 x^2 - 5 x^3 + 2 x^4)/(-1 + x)^3, {x, 0, 20}], x]
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CROSSREFS
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Essentially the same as A000096.
Sequence in context: A243166 A120740 A274282 * A000285 A042031 A041493
Adjacent sequences: A347550 A347551 A347552 * A347554 A347555 A347556
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KEYWORD
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nonn,easy
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AUTHOR
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Eric W. Weisstein, Sep 06 2021
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STATUS
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approved
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