A393385 Number of minimal edge covers in the n-necklace graph.

3, 7, 69, 571, 4729, 39227, 325305, 2697779, 22372865, 185539675, 1538693049, 12760485283, 105823565521, 877601969771, 7278012355305, 60357047577971, 500545068417473, 4151054028833851, 34424971171479513, 285488608899199939, 2367576298182197809, 19634470003296261131

Offset

0,1

Comments

The sequence has been extended to a(0) using the recurrence. - Andrew Howroyd, Feb 13 2026

Links

Andrew Howroyd, Table of n, a(n) for n = 0..500

Eric Weisstein's World of Mathematics, Minimal Edge Cover.

Eric Weisstein's World of Mathematics, Necklace Graph.

Index entries for linear recurrences with constant coefficients, signature (7,10,6).

Formula

G.f.: (3 - 14*x - 10*x^2)/(1 - 7*x - 10*x^2 - 6*x^3). - Andrew Howroyd, Feb 13 2026

a(n) = 7*a(n-1)+10*a(n-2)+6*a(n-3). - Eric W. Weisstein, Feb 18 2026

Mathematica

Table[RootSum[-6 - 10 # - 7 #^2 + #^3 &, #^n &], {n, 0, 20}] (* Eric W. Weisstein, Feb 18 2026 *)
RootSum[-6 - 10 # - 7 #^2 + #^3 &, #^Range[0, 20] &] (* Eric W. Weisstein, Feb 18 2026 *)
LinearRecurrence[{7, 10, 6}, {7, 69, 571}, {0, 20}] (* Eric W. Weisstein, Feb 18 2026 *)
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 *)

Crossrefs

Sequence in context: A120364 A088797 A165589 * A184316 A127177 A261136

Adjacent sequences: A393382 A393383 A393384 * A393386 A393387 A393388

Keyword

nonn

Author

Eric W. Weisstein, Feb 13 2026

Extensions

a(0) prepended and a(6) onward from Andrew Howroyd, Feb 13 2026

Status

approved