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

2,1

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.

Links

Table of n, a(n) for n=2..22.

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).

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)

Example

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

Mathematica

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

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.

Sequence in context: A138430 A366653 A164760 * A109774 A001657 A282185

Adjacent sequences: A335605 A335606 A335607 * A335609 A335610 A335611

Keyword

easy,nonn

Author

Steven Schlicker, Jun 15 2020

Status

approved