A393468 Number of minimal dominating sets in the n-necklace graph.

6, 4, 10, 61, 234, 919, 3601, 13983, 54730, 214324, 838145, 3278004, 12821685, 50150195, 196156243, 767240626, 3000958714, 11737853409, 45911076562, 179575146447, 702384591389, 2747285062359, 10745644611646, 42030177283824, 164395517168629, 643011469467644, 2515054893083509

Offset

0,1

Comments

The sequence has been extended to a(0) using the recurrence. - Andrew Howroyd, Feb 15 2026

Links

Andrew Howroyd, Table of n, a(n) for n = 0..1000

Eric Weisstein's World of Mathematics, Minimal Dominating Set.

Eric Weisstein's World of Mathematics, Necklace Graph.

Index entries for linear recurrences with constant coefficients, signature (4,-3,11,-6,16,-8).

Formula

G.f.: (6 - 20*x + 12*x^2 - 33*x^3 + 12*x^4 - 16*x^5)/(1 - 4*x + 3*x^2 - 11*x^3 + 6*x^4 - 16*x^5 + 8*x^6). - Andrew Howroyd, Feb 15 2026

Mathematica

Table[RootSum[8 - 16 # + 6 #^2 - 11 #^3 + 3 #^4 - 4 #^5 + #^6 &, #^n &], {n, 0, 26}] (* Eric W. Weisstein, Feb 16 2026 *)
RootSum[8 - 16 # + 6 #^2 - 11 #^3 + 3 #^4 - 4 #^5 + #^6 &, #^Range[0, 26] &] (* Eric W. Weisstein, Feb 16 2026 *)
LinearRecurrence[{4, -3, 11, -6, 16, -8}, {4, 10, 61, 234, 919, 3601}, 26] (* Eric W. Weisstein, Feb 16 2026 *)
CoefficientList[Series[-(-4 + 6 x - 33 x^2 + 24 x^3 - 80 x^4 + 48 x^5)/(1 - 4 x + 3 x^2 - 11 x^3 + 6 x^4 - 16 x^5 + 8 x^6), {x, 0, 25}], x] (* Eric W. Weisstein, Feb 16 2026 *)

Crossrefs

Cf. A392478, A393349.

Sequence in context: A116946 A357128 A141270 * A040032 A239394 A376614

Adjacent sequences: A393465 A393466 A393467 * A393469 A393470 A393471

Keyword

nonn,easy

Author

Eric W. Weisstein, Feb 15 2026

Extensions

a(0) prepended and a(7) onward from Andrew Howroyd, Feb 15 2026

Status

approved