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A335608
Number of sets (in the Hausdorff metric geometry) at each location between two sets defined by a complete bipartite graph K(3,n) (with n at least 2) missing one edge.
39
8, 104, 896, 6800, 49208, 349304, 2459696, 17261600, 120962408, 847130504, 5931094496, 41521204400, 290659059608, 2034645303704, 14242612785296, 99698576475200, 697890896260808, 4885238856628904, 34196679744812096, 239376781458914000, 1675637539948086008
OFFSET
2,1
COMMENTS
Number of {0,1} 3 X n matrices with one fixed zero entry and no zero rows or columns.
Number of edge covers of a complete bipartite graph K(3,n) (with n at least 2) missing one edge.
FORMULA
a(n) = 3*7^(n-1) - 5*3^(n-1) + 2.
From Stefano Spezia, Jul 04 2020: (Start)
G.f.: x^2*(8 + 16*x)/(1 - 11*x + 31*x^2 - 21*x^3).
a(n) = 11*a(n-1) - 31*a(n-2) + 21*a(n-3) for n > 4. (End)
EXAMPLE
For n = 2, a(2) = 8.
MATHEMATICA
Array[3*7^(# - 1) - 5*3^(# - 1) + 2 &, 21, 2] (* Michael De Vlieger, Jun 22 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: A138430 A366653 A164760 * A109774 A001657 A282185
KEYWORD
easy,nonn
AUTHOR
Steven Schlicker, Jun 15 2020
STATUS
approved