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A340405 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 the removed edges are incident to different vertices in the 6-point set and none of the removed edges are incident to the same vertex in the other set. 36
1084508, 91075250, 6565114436, 441241902314, 28686096681068, 1835221289891810, 116494017052053716, 7366358270603987354, 464926482693459729788, 29316615999089974986770, 1847760848280105290960996, 116434174169077299044440394, 7336135517363636128979098508 (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 the 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} 6 X n matrices 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(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.

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

FORMULA

a(n) = 29791*63^(n-3) - 31050*31^(n-3) + 12369*15^(n-3) - 2260*7^(n-3) + 19*3^(n-1) - 3.

From Alejandro J. Becerra Jr., Feb 13 2021: (Start)

G.f.: -2*x^4*(2773914255*x^5 - 4404958866*x^4 + 1920200130*x^3 - 308614840*x^2 + 19532855*x - 542254)/((1 - x)*(1 - 3*x)*(1 - 7*x)*(1 - 15*x)*(1 - 31*x)*(1 - 63*x)).

a(n) = 120*a(n-1) - 4593*a(n-2) + 69688*a(n-3) - 428787*a(n-4) + 978768*a(n-5) - 615195*a(n-6). (End)

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: A236449 A253467 A340132 * A258704 A224592 A252119

Adjacent sequences:  A340402 A340403 A340404 * A340406 A340407 A340408

KEYWORD

easy,nonn

AUTHOR

Rachel Wofford, Jan 06 2021

STATUS

approved

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Last modified October 28 04:43 EDT 2021. Contains 348313 sequences. (Running on oeis4.)