This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A343372 #22 Apr 06 2025 14:18:37
%S A343372 112,922,6880,49450,350032,2461882,17268160,120982090,847189552,
%T A343372 5931271642,41521735840,290660653930,2034650086672,14242627134202,
%U A343372 99698619521920,697891025400970,4885239244049392
%N A343372 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 exactly two removed edges are incident to the same vertex in the 3-point set and exactly two removed edges are incident to the same vertex in the other set.
%C A343372 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 exactly two removed edges are incident to the same point in A and exactly two removed edges are incident to the same point in B. So this sequence tells the number of sets at each location on the line segment between A' and B'.
%C A343372 Number of {0,1} 3 X n matrices (with n at least 4) with three fixed zero entries where exactly two zero entries occur in one row and exactly two zero entries occur in one column, with no zero rows or columns.
%C A343372 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 exactly two removed edges are incident to the same vertex in A and exactly two removed edges are incident to the same vertex in B.
%H A343372 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 A343372 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (11,-31,21).
%F A343372 a(n) = 3*7^(n-2) - 4*3^(n-2) + 1.
%F A343372 G.f.: 2*x^4*(56 - 155*x + 105*x^2)/(1 - 11*x + 31*x^2 - 21*x^3). - _Stefano Spezia_, Apr 13 2021
%t A343372 Drop[CoefficientList[Series[2 x^4*(56 - 155 x + 105 x^2)/(1 - 11 x + 31 x^2 - 21 x^3), {x, 0, 20}], x], 4] (* _Michael De Vlieger_, Apr 13 2021 *)
%t A343372 LinearRecurrence[{11,-31,21},{112,922,6880},20] (* _Harvey P. Dale_, Apr 06 2025 *)
%Y A343372 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 A343372 easy,nonn
%O A343372 4,1
%A A343372 _Steven Schlicker_, Apr 12 2021