A335609 - OEIS

%I #41 Jun 27 2023 11:10:29

%S 26,896,18458,316928,5049626,77860736,1182865178,17848076288,

%T 268458094106,4032033838976,60516655913498,908002911016448,

%U 13621815273480986,204339630665964416,3065181271854043418,45978326763617681408,689679155263179402266,10345217105634885213056

%N 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.

%C Number of {0,1} 4 X n matrices (with n at least 2) with one fixed zero entry and no zero rows or columns.

%C Number of edge covers of a K(4,n) complete bipartite graph (with n at least 2) missing one edge.

%H Colin Barker, <a href="/A335609/b335609.txt">Table of n, a(n) for n = 2..800</a>

%H Steven Schlicker, Roman Vasquez, and Rachel Wofford, <a href="https://cs.uwaterloo.ca/journals/JIS/VOL26/Wofford/wofford4.html">Integer Sequences from Configurations in the Hausdorff Metric Geometry via Edge Covers of Bipartite Graphs</a>, J. Int. Seq. (2023) Vol. 26, Art. 23.6.6.

%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (26,-196,486,-315).

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

%F From _Colin Barker_, Jun 23 2020: (Start)

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

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

%F (End)

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

%t Array[7*15^(# - 1) - 16*7^(# - 1) + 4*3^# - 3 &, 18, 2] (* _Michael De Vlieger_, Jun 22 2020 *)

%t LinearRecurrence[{26,-196,486,-315},{26,896,18458,316928},20] (* _Harvey P. Dale_, Aug 21 2021 *)

%o (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

%Y 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.

%K easy,nonn

%O 2,1

%A _Steven Schlicker_, Jun 15 2020