A392478 Number of dominating sets in the n-necklace graph.

3, 15, 199, 2799, 39443, 555855, 7833463, 110394159, 1555744931, 21924550287, 308974752679, 4354269371247, 61363142434739, 864768558952911, 12186870340755799, 171745153272253359, 2420342290330833731, 34109007973445479695, 480685905287198116999, 6774132502524173020143

Offset

0,1

Comments

The sequence has been extended to a(0) using the recurrence. - Andrew Howroyd, Feb 11 2026

Links

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

Eric Weisstein's World of Mathematics, Dominating Set.

Eric Weisstein's World of Mathematics, Necklace Graph.

Index entries for linear recurrences with constant coefficients, signature (15,-13,3).

Formula

G.f.: (3 - 30*x + 13*x^2)/(1 - 15*x + 13*x^2 - 3*x^3). - Andrew Howroyd, Feb 11 2026

a(n) = 15*a(n-1)-13*a(n-2)+3*a(n-3). - Eric W. Weisstein, Feb 12 2026

Mathematica

Table[RootSum[-3 + 13 # - 15 #^2 + #^3 &, #^n &], {n, 0, 20}]
RootSum[-3 + 13 # - 15 #^2 + #^3 &, #^Range[0, 20] &]
LinearRecurrence[{15, -13, 3}, {15, 199, 2799}, {0, 20}]
CoefficientList[Series[(-15 + 26 x - 9 x^2)/(-1 + 15 x - 13 x^2 + 3 x^3), {x, 0, 20}], x]

Crossrefs

Sequence in context: A068858 A280772 A166359 * A195515 A003505 A270354

Adjacent sequences: A392475 A392476 A392477 * A392479 A392480 A392481

Keyword

nonn,easy

Author

Eric W. Weisstein, Feb 11 2026

Extensions

a(0) prepended and a(7) onward from Andrew Howroyd, Feb 11 2026

Status

approved