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

2,1

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.

Links

Table of n, a(n) for n=2..17.

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).

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)

Example

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

Mathematica

Array[15*31^(# - 1) - 43*15^(# - 1) + 46*7^(# - 1) - 22*3^(# - 1) + 4 &, 16, 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: A216987 A283102 A259076 * A190931 A006202 A278736

Adjacent sequences: A335607 A335608 A335609 * A335611 A335612 A335613

Keyword

easy,nonn

Author

Steven Schlicker, Jun 15 2020

Status

approved