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A342850
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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 all three removed edges are incident to different vertices in the 3-point set and none of the removed edges are incident to the same vertex in the other set.
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36
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162, 1242, 9018, 64098, 451602, 3169962, 22215978, 155590578, 1089370242, 7626300282, 53386227738, 373709971458, 2615988932082, 18311979920202, 128184031628298, 897288737958738, 6281022715393122, 43967163656797722, 307770159544721658
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OFFSET
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4,1
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COMMENTS
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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 all three removed edges are incident to different points in A and 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 none of which are in the same row or column 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 all three removed edges are incident to different vertices in A and none of the removed edges are incident to the same vertex in B.
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REFERENCES
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S. Schlicker, R. Vasquez, R. Wofford, Integer Sequences from Configurations in the Hausdorff Metric Geometry via Edge Covers of Bipartite Graphs. In preparation.
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LINKS
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Table of n, a(n) for n=4..22.
Index entries for linear recurrences with constant coefficients, signature (10,-21).
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FORMULA
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a(n) = 27*7^(n-3) - 3^(n-1).
G.f.: 54*x^4*(3 - 7*x)/(1 - 10*x + 21*x^2). - Stefano Spezia, Mar 25 2021
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CROSSREFS
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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: A319915 A302731 A206145 * A304166 A213288 A302532
Adjacent sequences: A342847 A342848 A342849 * A342851 A342852 A342853
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KEYWORD
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easy,nonn
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AUTHOR
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Roman I. Vasquez, Mar 24 2021
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STATUS
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approved
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