A287474 - OEIS

%I #17 Feb 16 2025 08:33:46

%S 3,5,31,197,1123,6485,37567,217397,1258051,7280549,42133471,243831461,

%T 1411082659,8166108917,47258275711,273489449237,1582717053571,

%U 9159378096965,53006446688671,306754821216389,1775227849020643

%N Number of dominating sets in the n-web graph.

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

%H Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/DominatingSet.html">Dominating Set</a>

%H Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/WebGraph.html">Web Graph</a>

%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (5,3,9).

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

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

%t LinearRecurrence[{5, 3, 9}, {5, 31, 197}, {0, 20}]

%t Table[RootSum[-9 - 3 # - 5 #^2 + #^3 &, #^n &], {n, 0, 20}]

%t 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 *)

%o (PARI) polsym(-9 - 3*x - 5*x^2 + x^3, 25) \\ _Joerg Arndt_, May 26 2017

%K nonn,easy,changed

%O 0,1

%A _Eric W. Weisstein_, May 25 2017