A335608 Number of sets (in the Hausdorff metric geometry) at each location between two sets defined by a complete bipartite graph K(3,n) (with n at least 2) missing one edge.

8, 104, 896, 6800, 49208, 349304, 2459696, 17261600, 120962408, 847130504, 5931094496, 41521204400, 290659059608, 2034645303704, 14242612785296, 99698576475200, 697890896260808, 4885238856628904, 34196679744812096, 239376781458914000, 1675637539948086008

Offset: 2

Author

Steven Schlicker, Jun 15 2020

Keywords

• easy
• nonn

Comments

Number of {0,1} 3 X n matrices with one fixed zero entry and no zero rows or columns.

Number of edge covers of a complete bipartite graph K(3,n) (with n at least 2) missing one edge.

Examples

			For n = 2, a(2) = 8.
		

Links

• Steven Schlicker, Roman Vasquez, and Rachel Wofford, Integer Sequences from Configurations in the Hausdorff Metric Geometry via Edge Covers of Bipartite Graphs, J. Int. Seq. (2023) Vol. 26, Art. 23.6.6.
• Index entries for linear recurrences with constant coefficients, signature (11,-31,21).

Crossrefs

Sequences of segments from removing edges from bipartite graphs A335608-A335613, A337416-A337418, A340173-A340175, A340199-A340201, A340897-A340899, A342580, A342796, A342850, A340403-A340405, A340433-A340438, A341551-A341553, A342327-A342328, A343372-A343374, A343800. Polygonal chain sequences A152927, A152928, A152929, A152930, A152931, A152932, A152933, A152934, A152939. Number of {0,1} n X n matrices with no zero rows or columns A048291.

Programs

Mathematica

Array[3*7^(# - 1) - 5*3^(# - 1) + 2 &, 21, 2] (* Michael De Vlieger, Jun 22 2020 *)

Formula

a(n) = 3*7^(n-1) - 5*3^(n-1) + 2.

From Stefano Spezia, Jul 04 2020: (Start)

G.f.: x^2*(8 + 16*x)/(1 - 11*x + 31*x^2 - 21*x^3).

a(n) = 11*a(n-1) - 31*a(n-2) + 21*a(n-3) for n > 4. (End)