A392331 a(n) = 3^n*(4*n+1).

1, 15, 81, 351, 1377, 5103, 18225, 63423, 216513, 728271, 2421009, 7971615, 26040609, 84499119, 272629233, 875283327, 2798036865, 8910671247, 28281695697, 89494132959, 282429536481, 889130022255, 2792914305201, 8755315630911, 27395665038657, 85576149553743

Offset

0,2

Comments

For n >= 1, also the number of connected dominating sets in the n-necklace graph.

Links

Table of n, a(n) for n=0..25.

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

Eric Weisstein's World of Mathematics, Necklace Graph.

Index entries for linear recurrences with constant coefficients, signature (6,-9).

Formula

G.f.: (1+9*x)/(-1+3*x)^2.

a(n) = 6*a(n-1) - 9*a(n-2).

E.g.f.: exp(3*x)*(1 + 12*x). - Stefano Spezia, Feb 12 2026

Mathematica

Table[3^n (4 n + 1), {n, 0, 20}]
LinearRecurrence[{6, -9}, {15, 81}, {0, 20}]
CoefficientList[Series[(1 + 9 x)/(-1 + 3 x)^2, {x, 0, 20}], x]

Crossrefs

Cf. A000244, A016813.

Sequence in context: A309336 A266288 A213552 * A060581 A253222 A334244

Adjacent sequences: A392328 A392329 A392330 * A392332 A392333 A392334

Keyword

nonn,easy

Author

Eric W. Weisstein, Feb 12 2026

Status

approved