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 A333418 #30 Apr 05 2020 18:26:12 %S A333418 1,1,1,1,2,1,1,1,1,4,9,18,24,30,24,18,9,4,1,1,1,1,6,24,140,604,2596, %T A333418 9143 %N A333418 Irregular triangle: T(n,k) gives the number of ways to 2-color k edges of the n-cube up to rotation and reflection, with 0 <= k <= A001787(n). %C A333418 Conjecture: All rows are unimodal (increasing, then decreasing). %C A333418 Each row is a palindrome. %C A333418 A333333 is analogous with the restriction that the colorings must be connected. %H A333418 Mathematics Stack Exchange, <a href="https://math.stackexchange.com/q/3588391/121988">Number of 2-colorings of edges of the n-dimensional cube?</a>. %H A333418 Wikipedia, <a href="https://en.wikipedia.org/wiki/Hypercube">Hypercube</a> %F A333418 T(n,k) >= ceiling(binomial(A001787(n),k)/A000165(n)). %e A333418 Table begins: %e A333418 n\k| 0 1 2 3 4 5 6 7 8 9 10 11 12 ... %e A333418 ---+------------------------------------------------------- %e A333418 1| 1, 1; %e A333418 2| 1, 1, 2, 1, 1; %e A333418 3| 1, 1, 4, 9, 18, 24, 30, 24, 18, 9, 4, 1, 1; %e A333418 4| 1, 1, 6, 24, 140, 604, 2596, 9143, ... %e A333418 5| 1, 1, 8, 50, 608, ... %e A333418 6| 1, 1, 10, 89, ... %Y A333418 Row sums are A333444. %Y A333418 Cf. A001787, A060530, A199406, A331359, A333444, A333333. %K A333418 nonn,tabf,more %O A333418 1,5 %A A333418 _Peter Kagey_, Mar 20 2020