A287474 Number of dominating sets in the n-web graph.

3, 5, 31, 197, 1123, 6485, 37567, 217397, 1258051, 7280549, 42133471, 243831461, 1411082659, 8166108917, 47258275711, 273489449237, 1582717053571, 9159378096965, 53006446688671, 306754821216389, 1775227849020643

Offset: 0

Author

Eric W. Weisstein, May 25 2017

Keywords

• nonn
• easy

Comments

Extended to a(0)-a(2) using the recurrence.

Links

• Eric Weisstein's World of Mathematics, Dominating Set
• Eric Weisstein's World of Mathematics, Web Graph
• Index entries for linear recurrences with constant coefficients, signature (5,3,9).

Programs

Mathematica

LinearRecurrence[{5, 3, 9}, {5, 31, 197}, {0, 20}]
Table[RootSum[-9 - 3 # - 5 #^2 + #^3 &, #^n &], {n, 0, 20}]
CoefficientList[Series[(-3 + 10 x + 3 x^2)/(-1 + 5 x + 3 x^2 + 9 x^3), {x, 0, 20}], x] (* Eric W. Weisstein, Apr 17 2018 *)

PARI

polsym(-9 - 3*x - 5*x^2 + x^3, 25) \\ Joerg Arndt, May 26 2017

Formula

G.f.: (-3 + 10*x + 3*x^2)/(-1 + 5*x + 3*x^2 + 9*x^3).

a(n) = 5*a(n-1) + 3*a(n-2) + 9*a(n-3).