A335609 Number of sets (in the Hausdorff metric geometry) at each location between two sets defined by a K(4,n) (with n at least 2) complete bipartite graph missing one edge.

26, 896, 18458, 316928, 5049626, 77860736, 1182865178, 17848076288, 268458094106, 4032033838976, 60516655913498, 908002911016448, 13621815273480986, 204339630665964416, 3065181271854043418, 45978326763617681408, 689679155263179402266, 10345217105634885213056

Offset

2,1

Comments

Number of {0,1} 4 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(4,n) complete bipartite graph (with n at least 2) missing one edge.

Links

Colin Barker, Table of n, a(n) for n = 2..800

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 (26,-196,486,-315).

Formula

a(n) = 7*15^(n-1) - 16*7^(n-1) + 4*3^n - 3.

From Colin Barker, Jun 23 2020: (Start)

G.f.: 2*x^2*(13 + 110*x + 129*x^2) / ((1 - x)*(1 - 3*x)*(1 - 7*x)*(1 - 15*x)).

a(n) = 26*a(n-1) - 196*a(n-2) + 486*a(n-3) - 315*a(n-4) for n>5.

(End)

Example

For n = 3, a(2) = 26.

Mathematica

Array[7*15^(# - 1) - 16*7^(# - 1) + 4*3^# - 3 &, 18, 2] (* Michael De Vlieger, Jun 22 2020 *)
LinearRecurrence[{26, -196, 486, -315}, {26, 896, 18458, 316928}, 20] (* Harvey P. Dale, Aug 21 2021 *)

Prog

(PARI) Vec(2*x^2*(13 + 110*x + 129*x^2) / ((1 - x)*(1 - 3*x)*(1 - 7*x)*(1 - 15*x)) + O(x^20)) \\ Colin Barker, Jun 23 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: A357140 A333117 A263945 * A241871 A160261 A357376

Adjacent sequences: A335606 A335607 A335608 * A335610 A335611 A335612

Keyword

easy,nonn

Author

Steven Schlicker, Jun 15 2020

Status

approved