A335610 Number of sets (in the Hausdorff metric geometry) at each location between two sets defined by a K(5,n) (with n at least 2) complete bipartite graph missing one edge.

80, 6800, 316928, 11784608, 397551920, 12828154160, 405380093408, 12683426301248, 394943123789840, 12269641330477520, 380755304897252288, 11809363300986469088, 366179512530595589360, 11352903763691009133680, 351960100658771425777568, 10911064386177197162304128

Offset: 2

Author

Steven Schlicker, Jun 15 2020

Keywords

• easy
• nonn

Comments

Number of {0,1} 5 X n matrices (with n at least 2) with one fixed zero entry and no zero rows or columns.

Number of edge covers of a K(5,n) complete bipartite graph (with n at least 2) missing one edge.

Examples

			For n = 2, a(2) = 80.
		

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 (57,-1002,6562,-15381,9765).

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[15*31^(# - 1) - 43*15^(# - 1) + 46*7^(# - 1) - 22*3^(# - 1) + 4 &, 16, 2] (* Michael De Vlieger, Jun 22 2020 *)

Formula

a(n) = 15*31^(n-1) - 43*15^(n-1) + 46*7^(n-1) - 22*3^(n-1) + 4.

From Stefano Spezia, Jul 04 2020: (Start)

G.f.: 16*x^2*(5 + 140*x + 593*x^2 + 522*x^3)/(1 - 57*x + 1002*x^2 - 6562*x^3 + 15381*x^4 - 9765*x^5).

a(n) = 57*a(n-1) - 1002*a(n-2) + 6562*a(n-3) - 15381*a(n-4) + 9765*a(n-5) for n > 6. (End)