

A340898


Number of sets in the geometry determined by the Hausdorff metric at each location between two sets defined by a complete bipartite graph K(3,n) (with n at least 4) missing three edges, where all three removed edges are incident to the same vertex in the 3point set.


0



104, 1064, 8480, 62480, 446744, 3155384, 22172240, 155459360, 1088976584, 7625119304, 53382684800, 373699342640, 2615957045624, 18311884260824, 128183744650160, 897287877024320, 6281020132589864, 43967155908387944, 307770136299492320
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OFFSET

4,1


COMMENTS

Start with a complete bipartite graph K(3,n) with vertex sets A and B where A = 3 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 the same point in A. So this sequence gives the number of sets at each location on the line segment between A' and B'.
Number of {0,1} 3 X n matrices (with n at least 4) with three fixed zero entries all in the same row and no zero rows or columns.
Take a complete bipartite graph K(3,n) (with n at least 4) having parts A and B where A = 3. This sequence gives the number of edge covers of the graph obtained from this K(3,n) graph after removing three edges, where all three removed edges are incident same vertex in A.


LINKS



FORMULA

a(n) = 27*7^(n3)  29*3^(n3) + 2.
G.f.: 8*x^4*(13  10*x)/(1  11*x + 31*x^2  21*x^3).
a(n) = 11*a(n1)  31*a(n2) + 21*a(n3) for n > 6. (End)


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

nonn,easy


AUTHOR



STATUS

approved



