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 A343374 #26 Sep 01 2025 12:19:38
%S A343374 58984,2445394,86336272,2843754442,90733504504,2851869796354,
%T A343374 88998264600352,2767824089452282,85935878802252424,
%U A343374 2666013369738472114,82676439390965238832,2563420051241406849322,79472778433612932113944,2463757486872117920024674,76378002443759735050203712
%N A343374 Number of sets in the geometry determined by the Hausdorff metric at each location between two sets defined by a complete bipartite graph K(5,n) (with n at least 4) missing three edges, where exactly two removed edges are incident to the same vertex in the 5-point set and exactly two removed edges are incident to the same vertex in the other set.
%C A343374 Start with a complete bipartite graph K(5,n) with vertex sets A and B where |A| = 5 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 A343374 Number of {0,1} 5 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 A343374 Take a complete bipartite graph K(5,n) (with n at least 4) having parts A and B where |A| = 5. This sequence gives the number of edge covers of the graph obtained from this K(5,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 A343374 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 A343374 <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (57,-1002,6562,-15381,9765).
%F A343374 a(n) = 105*31^(n-2) - 217*15^(n-2) + 148*7^(n-2) - 13*3^(n-1) + 3.
%F A343374 G.f.: 2*x^4*(29492 - 458347*x + 3025391*x^2 - 7090641*x^3 + 4501665*x^4)/((1 - x)*(1 - 3*x)*(1 - 7*x)*(1 - 15*x)*(1 - 31*x)). - _Stefano Spezia_, Sep 01 2025
%Y A343374 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 A343374 easy,nonn,changed
%O A343374 4,1
%A A343374 _Steven Schlicker_, Apr 12 2021
%E A343374 Typo in a(14) corrected by _Georg Fischer_, Dec 08 2021