A393328 Number of total dominating sets in the n-necklace graph.

4, 11, 119, 1361, 15107, 167381, 1855379, 20567201, 227989475, 2527284269, 28015180979, 310550888681, 3442485501011, 38160272128613, 423010167661907, 4689107073005681, 51979188263107523, 576194138974848797, 6387165649999319987, 70802325606980963129, 784850368074841744307

Offset

0,1

Comments

The sequence has been extended to a(0) using the recurrence. - Andrew Howroyd, Feb 12 2026

Links

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

Eric Weisstein's World of Mathematics, Necklace Graph.

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

Index entries for linear recurrences with constant coefficients, signature (11,-1,21,6).

Formula

G.f.: (4 - 33*x + 2*x^2 - 21*x^3)/(1 - 11*x + x^2 - 21*x^3 - 6*x^4). - Andrew Howroyd, Feb 12 2026

a(n) = 11*a(n-1)-a(n-2)+21*a(n-3)+6*a(n-4). - Eric W. Weisstein, Feb 13 2026

Mathematica

Table[RootSum[-6 - 21 # + #^2 - 11 #^3 + #^4 &, #^n &], {n, 0, 20}]
RootSum[-6 - 21 # + #^2 - 11 #^3 + #^4 &, #^Range[0, 20] &]
LinearRecurrence[{11, -1, 21, 6}, {11, 119, 1361, 15107}, {0, 20}]
CoefficientList[Series[(-4 + 33 x - 2 x^2 + 21 x^3)/(-1 + 11 x - x^2 + 21 x^3 + 6 x^4), {x, 0, 20}], x]

Crossrefs

Cf. A392478.

Sequence in context: A267154 A320501 A214113 * A167418 A055979 A018242

Adjacent sequences: A393325 A393326 A393327 * A393329 A393330 A393331

Keyword

nonn,easy

Author

Eric W. Weisstein, Feb 11 2026

Extensions

a(0) prepended and a(7) onward from Andrew Howroyd, Feb 12 2026

Status

approved