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A341551 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 exactly two of the removed edges are incident to the same vertex in the 6-point set but none of the removed edges are incident to the same vertex in the other set. 36
996787, 87880249, 6458329435, 437811072433, 28577902283587, 1831839463314409, 116388761878654315, 7363089071153371873, 464825043098493809107, 29313469954934882953369, 1847663299656911486659195, 116431149842916469716759313, 7336041758469840870854326627 (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 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} 6 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(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 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.

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.

Index entries for linear recurrences with constant coefficients, signature (120,-4593,69688,-428787,978768,-615195).

FORMULA

a(n)= 29791*63^(n-3) - 34890*31^(n-3) + 14673*15^(n-3) - 2740*7^(n-3) + 211*3^(n-3) - 4.

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: A236034 A055617 A055618 * A216276 A252903 A289140

Adjacent sequences:  A341548 A341549 A341550 * A341552 A341553 A341554

KEYWORD

easy,nonn

AUTHOR

Steven Schlicker, Feb 14 2021

STATUS

approved

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Last modified November 29 13:17 EST 2021. Contains 349416 sequences. (Running on oeis4.)