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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.
1
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
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.
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
KEYWORD
easy,nonn
AUTHOR
Steven Schlicker, Jun 15 2020
STATUS
approved