%I #14 Jun 01 2023 11:11:57
%S 1,7,22,55,124,265,550,1123,2272,4573,9178,18391,36820,73681,147406,
%T 294859,589768,1179589,2359234,4718527,9437116,18874297,37748662,
%U 75497395,150994864,301989805,603979690,1207959463,2415919012,4831838113,9663676318,19327352731
%N a(n) = (9*2^n - 6*n - 10)/2.
%C Number of connected induced subgraphs in the (2*n-1)-triangular snake graph.
%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/TriangularSnakeGraph.html">Triangular Snake 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 (4,-5,2).
%F a(n) = (9*2^n - 6*n - 10)/2.
%F a(n) = 4*a(n-1) - 5*a(n-2) + 2*a(n-3).
%F G.f.: x*(-1 - 3*x + x^2)/((-1 + x)^2*(-1 + 2*x)).
%F E.g.f.: exp(x)*(5*cosh(x) + 4*sinh(x) - 3*x - 5). - _Stefano Spezia_, May 31 2023
%t Table[(9 2^n - 6 n - 10)/2, {n, 20}]
%t LinearRecurrence[{4, -5, 2}, {1, 7, 22}, 20]
%t CoefficientList[Series[(-1 - 3 x + x^2)/((-1 + x)^2 (-1 + 2 x)), {x, 0, 20}], x]
%K nonn,easy
%O 1,2
%A _Eric W. Weisstein_, Jun 08 2019