OFFSET
1,1
COMMENTS
For n > 1, also the number of (non-null) connected induced subgraphs in the n-cocktail party graph.
LINKS
Eric Weisstein's World of Mathematics, Cocktail Party Graph
Eric Weisstein's World of Mathematics, Connected Graph
Eric Weisstein's World of Mathematics, Vertex-Induced Subgraph
Index entries for linear recurrences with constant coefficients, signature (6, -9, 4).
FORMULA
a(n) = 4^n - n - 1.
a(n) = 6*a(n-1) - 9*a(n-2) + 4*a(n-3).
G.f.: ((-2 - x) x)/((-1 + x)^2 (-1 + 4 x)).
MATHEMATICA
Table[4^n - n - 1, {n, 20}]
LinearRecurrence[{6, -9, 4}, {2, 13, 60}, 20]
CoefficientList[Series[(-2 - x)/((-1 + x)^2 (-1 + 4 x)), {x, 0, 20}], x]
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Eric W. Weisstein, Aug 09 2017
STATUS
approved