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%I #5 Jun 09 2019 01:24:31
%S 3,6,14,30,60,116,222,426,824,1608,3162,6254,12420,24732,49334,98514,
%T 196848,393488,786738,1573206,3146108,6291876,12583374,25166330,
%U 50332200,100663896,201327242,402653886,805307124,1610613548,3221226342,6442451874,12884902880,25769804832
%N a(n) = 3*2^n + n^2 - n.
%C Number of connected induced subgraphs in the n-dipyramidal graph (for n >=3).
%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/DipyramidalGraph.html">Dipyramidal 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_04">Index entries for linear recurrences with constant coefficients</a>, signature (5, -9, 7, -2).
%F a(n) = 3*2^n + n^2 - n.
%F a(n) = 5*a(n-1) - 9*a(n-2) + 7*a(n-3) - 2*a(n-4).
%F G.f.: (3 - 9*x + 11*x^2 - 7*x^3)/((-1 + x)^3*(-1 + 2*x)).
%t Table[3 2^n + n^2 - n, {n, 0, 40}]
%t LinearRecurrence[{5, -9, 7, -2}, {6, 14, 30, 60}, {0, 20}]
%t CoefficientList[Series[(3 - 9 x + 11 x^2 - 7 x^3)/((-1 + x)^3 (-1 + 2 x)), {x, 0, 20}], x]
%K nonn,easy
%O 0,1
%A _Eric W. Weisstein_, Jun 08 2019