A291706 Number of connected dominating sets in the n-ladder graph.

3, 9, 24, 56, 136, 328, 792, 1912, 4616, 11144, 26904, 64952, 156808, 378568, 913944, 2206456, 5326856, 12860168, 31047192, 74954552, 180956296, 436867144, 1054690584, 2546248312, 6147187208, 14840622728, 35828432664, 86497488056, 208823408776, 504144305608

Offset

1,1

Links

Table of n, a(n) for n=1..30.

Eric Weisstein's World of Mathematics, Connected Dominating Set

Eric Weisstein's World of Mathematics, Ladder Graph

Index entries for linear recurrences with constant coefficients, signature (2, 1).

Formula

a(n) = 4 lucas(n - 1, 2) for n > 2.

a(n) = 2*a(n-1) + a(n-2) for n > 4.

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

Mathematica

Table[Piecewise[{{3^n, n == 1 || n == 2}}, 4 LucasL[n - 1, 2]], {n, 20}]
Join[{3, 9}, LinearRecurrence[{2, 1}, {24, 56}, 20]]
CoefficientList[Series[(-3 - 3 x - 3 x^2 + x^3)/(-1 + 2 x + x^2), {x, 0, 20}], x]

Crossrefs

Row 2 of A291872.

Sequence in context: A244504 A085739 A245762 * A089830 A258111 A360197

Adjacent sequences: A291703 A291704 A291705 * A291707 A291708 A291709

Keyword

nonn,easy

Author

Eric W. Weisstein, Aug 30 2017

Status

approved