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A290325
Number of minimal dominating sets (and maximal irredundant sets) in the complete tripartite graph K_{n,n,n}.
2
3, 15, 30, 51, 78, 111, 150, 195, 246, 303, 366, 435, 510, 591, 678, 771, 870, 975, 1086, 1203, 1326, 1455, 1590, 1731, 1878, 2031, 2190, 2355, 2526, 2703, 2886, 3075, 3270, 3471, 3678, 3891, 4110, 4335, 4566, 4803, 5046, 5295, 5550, 5811, 6078
OFFSET
1,1
COMMENTS
When n>1 the minimal dominating sets consist of either a single vertex from any two of the partitions or all vertices from just one of the partitions. When n=1 only the later are minimal. - Andrew Howroyd, Jul 27 2017
LINKS
Eric Weisstein's World of Mathematics, Complete Tripartite Graph
Eric Weisstein's World of Mathematics, Maximal Irredundant Set
Eric Weisstein's World of Mathematics, Minimal Dominating Set
FORMULA
a(n) = 3*n^2 + 3 for n > 1. - Andrew Howroyd, Jul 27 2017
From Colin Barker, Jul 27 2017: (Start)
G.f.: 3*x*(1 + 2*x - 2*x^2 + x^3) / (1 - x)^3.
a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) for n > 4. (End)
E.g.f.: 3((x^2 + x + 1)*exp(x) - (2*x + 1)) + 3*x. - G. C. Greubel, Aug 17 2017
MATHEMATICA
Rest[With[{nn = 50}, CoefficientList[Series[3 ((x^2 + x + 1)*Exp[x] - (2*x + 1)) + 3*x, {x, 0, nn}], x]*Range[0, nn]!]] (* or *) Table[3*(n^2 +1), {n, 1, 50}] (* G. C. Greubel, Aug 17 2017 *)
PROG
(PARI) Vec(3*x*(1 + 2*x - 2*x^2 + x^3) / (1 - x)^3 + O(x^60)) \\ Colin Barker, Jul 27 2017
CROSSREFS
Sequence in context: A087183 A297851 A298088 * A271326 A106354 A228308
KEYWORD
nonn,easy
AUTHOR
Eric W. Weisstein, Jul 27 2017
EXTENSIONS
a(6)-a(45) from Andrew Howroyd, Jul 27 2017
Maximal irredundant sets added to name by Eric W. Weisstein, Aug 17 2017
STATUS
approved