A269869 Number of matchings (not necessarily perfect) in the triangle graph of order n.

1, 4, 27, 425, 14278, 1054396, 169858667, 59811185171, 46012925161519, 77344464552678876, 284066030784415134855, 2279568155737623235728996, 39969481180418160836567285156, 1531253921482570179838977438893104, 128176575381689893022287259560629125869

Offset: 1

Author

Andrew Howroyd, Mar 06 2016

Keywords

• nonn

Comments

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.

References

• Samuel Dittmer, Hiram Golze, Grant Molnar, and Caleb Stanford, Puzzle and Proof: A Decade of Problems from the Utah Math Olympiad, CRC Press, 2025, p. 59.

Links

• Andrew Howroyd, Table of n, a(n) for n = 1..25
• Eric Weisstein's World of Mathematics, Independent Edge Set.
• Eric Weisstein's World of Mathematics, Matching.
• Eric Weisstein's World of Mathematics, Triangular Grid Graph.

Crossrefs

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

Row sums of A288852.