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 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). 2
 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, 9143 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,5 COMMENTS Conjecture: All rows are unimodal (increasing, then decreasing). Each row is a palindrome. A333333 is analogous with the restriction that the colorings must be connected. LINKS Mathematics Stack Exchange, Number of 2-colorings of edges of the n-dimensional cube?. Wikipedia, Hypercube FORMULA T(n,k) >= ceiling(binomial(A001787(n),k)/A000165(n)). EXAMPLE Table begins: n\k| 0  1   2   3    4    5     6     7   8  9 10 11 12 ... ---+-------------------------------------------------------   1| 1, 1;   2| 1, 1,  2,  1,   1;   3| 1, 1,  4,  9,  18,  24,   30,   24, 18, 9, 4, 1, 1;   4| 1, 1,  6, 24, 140, 604, 2596, 9143, ...   5| 1, 1,  8, 50, 608, ...   6| 1, 1, 10, 89, ... CROSSREFS Row sums are A333444. Cf. A001787, A060530, A199406, A331359, A333444, A333333. Sequence in context: A174547 A119326 A219866 * A212363 A212382 A274835 Adjacent sequences:  A333415 A333416 A333417 * A333419 A333420 A333421 KEYWORD nonn,tabf,more AUTHOR Peter Kagey, Mar 20 2020 STATUS approved

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Last modified September 17 22:42 EDT 2021. Contains 347489 sequences. (Running on oeis4.)