# Greetings from The On-Line Encyclopedia of Integer Sequences! http://oeis.org/ Search: id:a343373 Showing 1-1 of 1 %I A343373 #16 Jun 27 2023 11:47:29 %S A343373 3112,58984,978064,15345952,234980152,3558436504,53613281824, %T A343373 805858151632,12099490097992,181573692295624,2724174818398384, %U A343373 40866608458275712,613027030583891032,9195600786027620344 %N A343373 Number of sets in the geometry determined by the Hausdorff metric at each location between two sets defined by a complete bipartite graph K(4,n) (with n at least 4) missing three edges, where exactly two removed edges are incident to the same vertex in the 4-point set and exactly two removed edges are incident to the same vertex in the other set. %C A343373 Start with a complete bipartite graph K(4,n) with vertex sets A and B where |A| = 4 and |B| is at least 4. We can arrange the points in sets A and B such that h(A,B) = d(a,b) for all a in A and b in B, where h is the Hausdorff metric. The pair [A,B] is a configuration. Then a set C is between A and B at location s if h(A,C) = h(C,B) = h(A,B) and h(A,C) = s. Call a pair ab, where a is in A and b is in B an edge. This sequence provides the number of sets between sets A' and B' at location s in a new configuration [A',B'] obtained from [A,B] by removing three edges, where exactly two removed edges are incident to the same point in A and exactly two removed edges are incident to the same point in B. So this sequence tells the number of sets at each location on the line segment between A' and B'. %C A343373 Number of {0,1} 4 X n matrices (with n at least 4) with three fixed zero entries where exactly two zero entries occur in one row and exactly two zero entries occur in one column, with no zero rows or columns. %C A343373 Take a complete bipartite graph K(4,n) (with n at least 4) having parts A and B where |A| = 4. This sequence gives the number of edge covers of the graph obtained from this K(4,n) graph after removing three edges, where exactly two removed edges are incident to the same vertex in A and exactly two removed edges are incident to the same vertex in B. %H A343373 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. %H A343373 Index entries for linear recurrences with constant coefficients, signature (26,-196,486,-315). %F A343373 a(n) = 21*15^(n-2) - 36*7^(n-2) + 17*3^(n-2) - 2. %F A343373 G.f.: 8*x^4*(389 - 2741*x + 6804*x^2 - 4410*x^3)/(1 - 26*x + 196*x^2 - 486*x^3 + 315*x^4). - _Stefano Spezia_, Apr 13 2021 %Y A343373 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 A343373 easy,nonn %O A343373 4,1 %A A343373 _Steven Schlicker_, Apr 12 2021 # Content is available under The OEIS End-User License Agreement: http://oeis.org/LICENSE