A393385 - OEIS

%I #12 Feb 18 2026 11:30:12

%S 3,7,69,571,4729,39227,325305,2697779,22372865,185539675,1538693049,

%T 12760485283,105823565521,877601969771,7278012355305,60357047577971,

%U 500545068417473,4151054028833851,34424971171479513,285488608899199939,2367576298182197809,19634470003296261131

%N Number of minimal edge covers in the n-necklace graph.

%C The sequence has been extended to a(0) using the recurrence. - _Andrew Howroyd_, Feb 13 2026

%H Andrew Howroyd, <a href="/A393385/b393385.txt">Table of n, a(n) for n = 0..500</a>

%H Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/MinimalEdgeCover.html">Minimal Edge Cover</a>.

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

%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (7,10,6).

%F G.f.: (3 - 14*x - 10*x^2)/(1 - 7*x - 10*x^2 - 6*x^3). - _Andrew Howroyd_, Feb 13 2026

%F a(n) = 7*a(n-1)+10*a(n-2)+6*a(n-3). - _Eric W. Weisstein_, Feb 18 2026

%t Table[RootSum[-6 - 10 # - 7 #^2 + #^3 &, #^n &], {n, 0, 20}] (* _Eric W. Weisstein_, Feb 18 2026 *)

%t RootSum[-6 - 10 # - 7 #^2 + #^3 &, #^Range[0, 20] &] (* _Eric W. Weisstein_, Feb 18 2026 *)

%t LinearRecurrence[{7, 10, 6}, {7, 69, 571}, {0, 20}] (* _Eric W. Weisstein_, Feb 18 2026 *)

%t CoefficientList[Series[(-3 + 14 x + 10 x^2)/(-1 + 7 x + 10 x^2 + 6 x^3), {x, 0, 20}], x] (* _Eric W. Weisstein_, Feb 18 2026 *)

%K nonn

%O 0,1

%A _Eric W. Weisstein_, Feb 13 2026

%E a(0) prepended and a(6) onward from _Andrew Howroyd_, Feb 13 2026