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 A341850 Array read by antidiagonals: T(n,m) is the number of maximum matchings in the rook graph K_n X K_m. 5
 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 3, 2, 3, 1, 1, 3, 4, 4, 3, 1, 1, 15, 16, 72, 16, 15, 1, 1, 15, 56, 132, 132, 56, 15, 1, 1, 105, 376, 7020, 2016, 7020, 376, 105, 1, 1, 105, 1912, 17280, 44928, 44928, 17280, 1912, 105, 1, 1, 945, 17984, 1920240, 1551744, 22615200, 1551744, 1920240, 17984, 945, 1 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 0,12 COMMENTS In the case that both m and n are odd a single vertex is not covered, otherwise the maximum matchings are perfect matchings. LINKS Andrew Howroyd, Table of n, a(n) for n = 0..527 Eric Weisstein's World of Mathematics, Maximum Independent Edge Set Eric Weisstein's World of Mathematics, Rook Graph FORMULA T(n,m) = T(m,n). EXAMPLE Array begins: ====================================================== n\m | 0 1 2 3 4 5 6 ----+------------------------------------------------- 0 | 1 1 1 1 1 1 1 ... 1 | 1 1 1 3 3 15 15 ... 2 | 1 1 2 4 16 56 376 ... 3 | 1 3 4 72 132 7020 17280 ... 4 | 1 3 16 132 2016 44928 1551744 ... 5 | 1 15 56 7020 44928 22615200 243319680 ... 6 | 1 15 376 17280 1551744 243319680 61903180800 ... ... CROSSREFS Rows n=1..4 are A133221(n+1), A081919, A341851, A341852. Main diagonal is A289197. Cf. A270227 (matchings), A286070, A341847 (maximal matchings). Sequence in context: A085747 A106693 A107335 * A341847 A200223 A236228 Adjacent sequences: A341847 A341848 A341849 * A341851 A341852 A341853 KEYWORD nonn,tabl AUTHOR Andrew Howroyd, Feb 21 2021 STATUS approved

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Last modified May 18 11:53 EDT 2024. Contains 372630 sequences. (Running on oeis4.)