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A290718 a(n) = 2^(n + 1) + 4^(n - 1) - 2. 0

%I #5 Aug 09 2017 11:38:35

%S 3,10,30,94,318,1150,4350,16894,66558,264190,1052670,4202494,16793598,

%T 67141630,268500990,1073872894,4295229438,17180393470,68720525310,

%U 274880004094,1099515822078,4398054899710,17592202821630,70368777732094,281475043819518,1125900041060350,4503599895805950,18014399046352894,72057595111669758

%N a(n) = 2^(n + 1) + 4^(n - 1) - 2.

%C For n > 2, also the number of connected (non-null) induced subgraphs in the n-barbell graph.

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/BarbellGraph.html">Barbell Graph</a>

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/ConnectedGraph.html">Connected Graph</a>

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/Vertex-InducedSubgraph.html">Vertex-Induced Subgraph</a>

%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (7,-14,8).

%F a(n) = 2^(n + 1) + 4^(n - 1) - 2.

%F a(n) = 7*a(n-1) - 14*a(n-2) + 8*a(n-3).

%F G.f.: (x (-3 + 11 x - 2 x^2))/(-1 + 7 x - 14 x^2 + 8 x^3).

%t Table[2^(n + 1) + 4^(n - 1) - 2, {n, 20}]

%t LinearRecurrence[{7, -14, 8}, {3, 10, 30}, 40]

%t CoefficientList[Series[(-3 + 11 x - 2 x^2)/(-1 + 7 x - 14 x^2 + 8 x^3), {x, 0, 20}], x]

%o (PARI) a(n)=2^(n+1)+4^(n-1)-2 \\ _Charles R Greathouse IV_, Aug 09 2017

%K nonn,easy

%O 1,1

%A _Eric W. Weisstein_, Aug 09 2017

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Last modified March 28 18:04 EDT 2024. Contains 371254 sequences. (Running on oeis4.)