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A340435 Number of sets in the geometry determined by the Hausdorff metric at each location between two sets defined by a complete bipartite graph K(6,n) (with n at least 4) missing three edges, where all three removed edges are incident to different vertices in the 6-point set but all three removed edges are incident to the same vertex in the other set. 0
1014458, 85045184, 6126191066, 411615281120, 26756164505978, 1711634190402944, 108645469309633946, 6869952591587660960, 433592445465504586298, 27340695032306205303104, 1723219625722022031240026, 108586272500880714880450400, 6841661762270647247773447418 (list; graph; refs; listen; history; text; internal format)
OFFSET

4,1

COMMENTS

Start with a complete bipartite graph K(6,n) with vertex sets A and B where |A| = 6 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 but all three 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} 6 X n matrices (with n at least 4) with three fixed zero entries all of which are in the same column with no zero rows or columns.

Take a complete bipartite graph K(6,n) (with n at least 4) having parts A and B where |A| = 6. This sequence gives the number of edge covers of the graph obtained from this K(6,n) graph after removing three edges, where the removed edges are incident to different vertices in A and none of the removed edges are incident to the same vertex in B.

REFERENCES

S. Schlicker, R. Vasquez, R. Wofford, Integer Sequences from Configurations in the Hausdorff Metric Geometry via Edge Covers of Bipartite Graphs. In preparation.

LINKS

Table of n, a(n) for n=4..16.

FORMULA

a(n) = 7*63^(n-1) - 30*31^(n-1) + 51*15^(n-1) - 43*7^(n-1) + 6*3^(n) - 3.

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: A096931 A210274 A252916 * A066598 A212940 A232144

Adjacent sequences:  A340432 A340433 A340434 * A340436 A340437 A340438

KEYWORD

easy,nonn

AUTHOR

Rachel Wofford, Jan 07 2021

STATUS

approved

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Last modified May 28 09:09 EDT 2022. Contains 354112 sequences. (Running on oeis4.)