

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
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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.


LINKS



FORMULA

a(n) = 49*15^(n2)  76*7^(n2) + 10*3^(n1)  3.
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(n1)  196*a(n2) + 486*a(n3)  315*a(n4) for n>6.
(End)


MAPLE

a:= proc(n) 49*15^(n2)76*7^(n2)+10*3^(n1)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 A335608A335613, A337416A337418, A340173A340175, A340199A340201, A340897A340899, A342580, A342796, A342850, A340403A340405, A340433A340438, A341551A341553, A342327A342328, A343372A343374, 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.


KEYWORD

easy,nonn


AUTHOR



STATUS

approved



