%I #20 Jun 19 2017 09:27:57

%S 1,4,27,425,14278,1054396,169858667,59811185171,46012925161519,

%T 77344464552678876,284066030784415134855,2279568155737623235728996,

%U 39969481180418160836567285156,1531253921482570179838977438893104,128176575381689893022287259560629125869

%N Number of matchings (not necessarily perfect) in the triangle graph of order n.

%C The triangle graph of order n has n rows with i vertices in row i. Each vertex is connected to the neighbors in the same row and up to two vertices in each of the neighboring rows. The graph has A000217(n) vertices and 3*A000217(n-1) edges altogether.

%H Andrew Howroyd, <a href="/A269869/b269869.txt">Table of n, a(n) for n = 1..25</a>

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/IndependentEdgeSet.html">Independent Edge Set</a>

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

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

%Y Cf. A000217, A028420, A039907, A112676, A178446.

%Y Row sums of A288852.

%K nonn

%O 1,2

%A _Andrew Howroyd_, Mar 06 2016