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 A341552 #16 Jun 27 2023 11:44:28
%S A341552 129,975,7041,49935,351489,2466255,17281281,121021455,847307649,
%T A341552 5931625935,41522798721,290663842575,2034659652609,14242655832015,
%U A341552 99698705615361,697891283681295,4885240018890369,34196683231596495,239376791919267201,1675637571329145615
%N A341552 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 different vertices in the 3 point set but exactly two removed edges are incident to the same vertex in the other set.
%C A341552 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 different points in A but 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 A341552 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 column and no row has more than one zero entry, with no zero rows or columns.
%C A341552 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 to different vertices in A but exactly two removed edges are incident to the same vertex in B.
%H A341552 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 A341552 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (10,-21).
%F A341552 a(n) = 3*7^(n-2)-2*3^(n-2).
%F A341552 G.f.: 3*x^4*(43 - 105*x)/(1 - 10*x + 21*x^2). - _Stefano Spezia_, Feb 14 2021
%Y A341552 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 A341552 easy,nonn
%O A341552 4,1
%A A341552 _Steven Schlicker_, Feb 14 2021