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A335613 Number of sets (in the Hausdorff metric geometry) at each location between two sets defined by a complete bipartite graph K(4,n) (with n at least 3) missing two edges, where the removed edges are incident to the same vertex in the four point part. 39
290, 7568, 140114, 2300576, 35939330, 549221168, 8309585714, 125143712576, 1880658325730, 28234402793168, 423687765591314, 6356518634756576, 95356194832648130, 1430401830434093168, 21456439814417820914, 321849483728499752576, 4827762461533785786530 (list; graph; refs; listen; history; text; internal format)
OFFSET

3,1

COMMENTS

The Hausdorff metric defines a distance between sets. Using this distance we can define line segments with sets as endpoints. Create two sets from the vertices of the parts A and B (with |A| = 4) of a complete bipartite graph K(4,n) (with n at least 3) missing two edges, where the removed edges are incident to the same point in A. Points in the sets A and B that correspond to vertices that are connected by edges are the same Euclidean distance apart. This sequence tells the number of sets at each location on the line segment between A and B.

Number of {0,1} 4 X n (with n at least 3) matrices with two fixed zero entries in the same row and no zero rows or columns.

Take a complete bipartite graph K(4,n) (with n at least 3) having parts A and B where |A| = 4. This sequence gives the number of edge covers of the graph obtained from this K(4,n) graph after removing two edges, where the two removed edges are incident to the same vertex in A.

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=3..19.

Index entries for linear recurrences with constant coefficients, signature (26,-196,486,-315).

FORMULA

a(n) = 49*15^(n-2) - 76*7^(n-2) + 10*3^(n-1) - 3.

From Colin Barker, Jul 17 2020: (Start)

G.f.: 2*x^3*(145 + 14*x + 93*x^2) / ((1 - x)*(1 - 3*x)*(1 - 7*x)*(1 - 15*x)).

a(n) = 26*a(n-1) - 196*a(n-2) + 486*a(n-3) - 315*a(n-4) for n>6.

(End)

MAPLE

a:= proc(n) 49*15^(n-2)-76*7^(n-2)+10*3^(n-1)-3 end proc: seq(a(n), n=3..20);

PROG

(PARI) Vec(2*x^3*(145 + 14*x + 93*x^2) / ((1 - x)*(1 - 3*x)*(1 - 7*x)*(1 - 15*x)) + O(x^22)) \\ Colin Barker, Jul 17 2020

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: A108881 A186547 A237741 * A186548 A091740 A098250

Adjacent sequences:  A335610 A335611 A335612 * A335614 A335615 A335616

KEYWORD

easy,nonn

AUTHOR

Steven Schlicker, Jul 16 2020

STATUS

approved

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Last modified May 19 23:40 EDT 2022. Contains 353847 sequences. (Running on oeis4.)