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 A329255 Irregular triangle read by rows: T(n,k) is greatest positive integer <= n that have a partition into k consecutive parts, 1 <= k <= A003056(n), n >= 1. 0
 1, 2, 3, 3, 4, 3, 5, 5, 6, 5, 6, 7, 7, 6, 8, 7, 6, 9, 9, 9, 10, 9, 9, 10, 11, 11, 9, 10, 12, 11, 12, 10, 13, 13, 12, 10, 14, 13, 12, 14, 15, 15, 15, 14, 15, 16, 15, 15, 14, 15, 17, 17, 15, 14, 15, 18, 17, 18, 18, 15, 19, 19, 18, 18, 15, 20, 19, 18, 18, 20, 21, 21, 21, 18, 20, 21, 22, 21, 21, 22, 20, 21 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS T(n,k) is also the positive integer whose partition into k consecutive parts is associated to the k-th vertex, from left to right, of the largest Dyck path of the symmetric representation of sigma(n). For more information see A237593. Also this triangle can be constructed replacing every zero of triangle A285891 with the previous positive integer from the same column. LINKS Table of n, a(n) for n=1..82. EXAMPLE Triangle begins: 1; 2; 3, 3; 4, 3; 5, 5; 6, 5, 6; 7, 7, 6; 8, 7, 6; 9, 9, 9; 10, 9, 9, 10; 11, 11, 9, 10; 12, 11, 12, 10; 13, 13, 12, 10; 14, 13, 12, 14; 15, 15, 15, 14, 15; 16, 15, 15, 14, 15; 17, 17, 15, 14, 15; 18, 17, 18, 18, 15; 19, 19, 18, 18, 15; 20, 19, 18, 18, 20; 21, 21, 21, 18, 20, 21; 22, 21, 21, 22, 20, 21; 23, 23, 21, 22, 20, 21; 24, 23, 24, 22, 20, 21; 25, 25, 24, 22, 25, 21; 26, 25, 24, 26, 25, 21; 27, 27, 27, 26, 25, 27; 28, 27, 27, 26, 25, 27, 28; ... CROSSREFS Column k stars with A000217(k) in the row A000217(k). Row n has length A003056(n). Cf. A196020, A204217, A211343, A235791, A236104, A235791, A237048, A237591, A237593, A285900, A285914, A285891, A286000, A286001, A286013, A299765, A328361, A328365, A328371. Sequence in context: A255239 A316339 A186971 * A262535 A096827 A298321 Adjacent sequences: A329252 A329253 A329254 * A329256 A329257 A329258 KEYWORD nonn,tabf AUTHOR Omar E. Pol, Nov 09 2019 STATUS approved

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Last modified September 16 08:55 EDT 2024. Contains 375959 sequences. (Running on oeis4.)