A027740 Number of independent subsets of nodes in graph formed from n-fold subdivision of triangle.

1, 2, 4, 14, 60, 384, 3318, 40638, 689636, 16383974, 542420394, 25075022590, 1617185558560, 145563089994148, 18283036276489970, 3204638749437865046, 783848125594781710150, 267554112823378352976752

Offset: 0

Author

R. H. Hardin

Keywords

• nonn
• nice

Comments

In other words, number of independent vertex sets (and vertex covers) in the (n-1)-triangular grid graph. - Eric W. Weisstein, Jun 14 2017

Number of planar n X n X n binary triangular grids with no more than 1 one in any similarly oriented 2 X 2 X 2 subtriangle. - R. H. Hardin, Dec 27 2008

Links

• Liang Kai, Table of n, a(n) for n = 0..40
• Kai Liang, Independent Set Enumeration and Estimation of Related Constants of Grid Graphs, arXiv:2507.04007 [math.CO], 2025. See pp. 1, 10.
• Eric Weisstein's World of Mathematics, Independent Vertex Set
• Eric Weisstein's World of Mathematics, Triangular Grid Graph
• Eric Weisstein's World of Mathematics, Vertex Cover

Crossrefs

Cf. A239567, A239438, A287064.