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.

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).

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%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