A335608 - OEIS

%I #34 Jun 27 2023 11:10:38

%S 8,104,896,6800,49208,349304,2459696,17261600,120962408,847130504,

%T 5931094496,41521204400,290659059608,2034645303704,14242612785296,

%U 99698576475200,697890896260808,4885238856628904,34196679744812096,239376781458914000,1675637539948086008

%N 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.

%C Number of {0,1} 3 X n matrices with one fixed zero entry and no zero rows or columns.

%C Number of edge covers of a complete bipartite graph K(3,n) (with n at least 2) missing one edge.

%H Steven Schlicker, Roman Vasquez, and Rachel Wofford, <a href="https://cs.uwaterloo.ca/journals/JIS/VOL26/Wofford/wofford4.html">Integer Sequences from Configurations in the Hausdorff Metric Geometry via Edge Covers of Bipartite Graphs</a>, J. Int. Seq. (2023) Vol. 26, Art. 23.6.6.

%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (11,-31,21).

%F a(n) = 3*7^(n-1) - 5*3^(n-1) + 2.

%F From _Stefano Spezia_, Jul 04 2020: (Start)

%F G.f.: x^2*(8 + 16*x)/(1 - 11*x + 31*x^2 - 21*x^3).

%F a(n) = 11*a(n-1) - 31*a(n-2) + 21*a(n-3) for n > 4. (End)

%e For n = 2, a(2) = 8.

%t Array[3*7^(# - 1) - 5*3^(# - 1) + 2 &, 21, 2] (* _Michael De Vlieger_, Jun 22 2020 *)

%Y 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.

%K easy,nonn

%O 2,1

%A _Steven Schlicker_, Jun 15 2020