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

1,2

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.

Sequence in context: A271615 A271616 A123672 * A119030 A356806 A120093

Adjacent sequences: A269866 A269867 A269868 * A269870 A269871 A269872

Keyword

nonn,changed

Author

Andrew Howroyd, Mar 06 2016

Status

approved