A347553 Number of minimum dominating sets in the n-cycle complement graph.

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

Offset

3,2

Links

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).

Formula

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)

Mathematica

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]

Crossrefs

Essentially the same as A000096.

Sequence in context: A363269 A120740 A274282 * A000285 A042031 A041493

Adjacent sequences: A347550 A347551 A347552 * A347554 A347555 A347556

Keyword

nonn,easy

Author

Eric W. Weisstein, Sep 06 2021

Status

approved