cp's OEIS Frontend

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.

A364505 T(n, k) = number of k-dimensional faces in the BME polytope on n species, 0 <= k <= binomial(n, 2) - n.

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%I A364505 #19 Jul 29 2023 02:59:38
%S A364505 3,3,1,15,105,250,210,52,1,105,5460,105945,635265,1715455,2373345,
%T A364505 1742445,640140,90262,1
%N A364505 T(n, k) = number of k-dimensional faces in the BME polytope on n species, 0 <= k <= binomial(n, 2) - n.
%C A364505 The balanced minimum evolution (BME) polytope of order n is the convex hull of the BME vectors of all phylogenetic trees on n species. The BME polytope of order n has dimension binomial(n, 2) - n.
%H A364505 Maria Angelica Cueto and Frederick A. Matsen, <a href="https://doi.org/10.1007/s11538-010-9556-x">Polyhedral geometry of phylogenetic rogue taxa</a>, Bull. Math. Biol., 73 (2011), 1202-1226.
%H A364505 K. Eickmeyer, P. Huggins, L. Pachter, and R. Yoshida, <a href="https://doi.org/10.1186%2F1748-7188-3-5">On the optimality of the neighbor-joining algorithm</a>, Algorithms Mol Biol. 3 (2008), Article number 5.
%H A364505 Stefan Forcey, <a href="https://sforcey.github.io/sf34/hedra.htm#BME">Balanced Minimum Evolution Polytope</a>, Encyclopedia of Combinatorial Polytope Sequences (Hedra Zoo).
%e A364505 Table begins:
%e A364505     3,    3,      1;
%e A364505    15,  105,    250,    210,      52,       1;
%e A364505   105, 5460, 105945, 635265, 1715455, 2373345, 1742445, 640140, 90262, 1;
%Y A364505 First column T(n, 0) is A001147.
%Y A364505 Next-to-last entry T(n, binomial(n, 2) - n - 1) in each row is A364441.
%K A364505 nonn,tabf,more
%O A364505 4,1
%A A364505 _Harry Richman_, Jul 26 2023