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
Examples
For n = 3, a(2) = 26.
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).
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
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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 *)
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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
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)
Comments