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A291706
Number of connected dominating sets in the n-ladder graph.
1
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
Eric Weisstein's World of Mathematics, Connected Dominating Set
Eric Weisstein's World of Mathematics, Ladder Graph
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
KEYWORD
nonn,easy
AUTHOR
Eric W. Weisstein, Aug 30 2017
STATUS
approved