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A340436 Number of sets in the geometry determined by the Hausdorff metric at each location between two sets defined by a complete bipartite graph K(3,n) (with n at least 4) missing three edges, where exactly two of the removed edges are incident to the same vertex in the 3-point set but none of the removed edges are incident to the same vertex in the other set. 0
151, 1207, 8911, 63775, 450631, 3167047, 22207231, 155564335, 1089291511, 7626064087, 53385519151, 373707845695, 2615982554791, 18311960788327, 128183974232671, 897288565771855, 6281022198832471, 43967162107115767, 307770154895675791 (list; graph; refs; listen; history; text; internal format)
OFFSET
4,1
COMMENTS
Start with a complete bipartite graph K(3,n) with vertex sets A and B where |A| = 3 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 of the removed edges are incident to the same point in A but none of the 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'.
Number of {0,1} 3 X n matrices (with n at least 4) with three fixed zero entries where exactly two zero entries occur in one row and no column has more than one zero entry, with no zero rows or columns.
Take a complete bipartite graph K(3,n) (with n at least 4) having parts A and B where |A| = 3. This sequence gives the number of edge covers of the graph obtained from this K(3,n) graph after removing three edges, where exactly two of the removed edges are incident to the same vertex in A but none of the removed edges are incident to the same vertex in B.
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) = 27*7^(n-3) - 13*3^(n-3) + 1.
G.f.: x^4*(151 - 454*x + 315*x^2)/(1 - 11*x + 31*x^2 - 21*x^3). - Stefano Spezia, Apr 10 2021
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: A139640 A334836 A130870 * A211555 A143012 A250375
KEYWORD
easy,nonn
AUTHOR
Rachel Wofford, Apr 02 2021
STATUS
approved

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Last modified June 24 23:28 EDT 2024. Contains 373691 sequences. (Running on oeis4.)