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 A030717 Table with T(1,1) = 1; for n>1, T(n,k) is the number of k's in rows 1 through n-1. 14
 1, 1, 2, 2, 1, 3, 2, 3, 3, 1, 4, 3, 3, 4, 3, 5, 1, 5, 3, 6, 2, 1, 6, 4, 7, 2, 2, 1, 7, 6, 7, 3, 2, 2, 1, 8, 8, 8, 3, 2, 3, 3, 8, 9, 11, 3, 2, 3, 3, 3, 8, 10, 15, 3, 2, 3, 3, 4, 1, 0, 1, 10, 11, 18, 4, 2, 3, 3, 5, 1, 1, 1, 0, 0, 0, 1, 14, 12, 20, 5, 3, 3, 3, 5, 1, 2, 2, 0, 0, 0, 1, 0, 0, 1, 17, 14, 23, 5, 5 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,3 COMMENTS Equivalently, row 1, where, at stage k>1, write i in row 1 and j in row 2, where i is the number of j's in row 1, for j=1,2,...,m, where m=max number in row 1 from stages 1 to k-1; state 1 is 1 in row 1. LINKS Franklin T. Adams-Watters, First 32 rows, flattened EXAMPLE 1; 1; 2; 2, 1; 3, 2; 3, 3, 1; 4, 3, 3; PROG (Haskell) import Data.List (sort, group) a030717 n k = a030717_tabf !! (n-1) !! (k-1) a030717_row n = a030717_tabf !! (n-1) a030717_tabf = [1] : f [1] where    f xs = ys : f ((filter (> 0) ys) ++ xs) where           ys = h (group \$ sort xs) [1..] where                h [] _ = []                h vss'@(vs:vss) (w:ws)                  | head vs == w = (length vs) : h vss ws                  | otherwise    = 0 : h vss' ws -- Reinhard Zumkeller, Dec 28 2014 CROSSREFS Cf. A126027 (row lengths), A006920, A030718 (column numbers). Cf. A174382. Cf. A253170 (row sums). Sequence in context: A128180 A209279 A074754 * A071285 A008678 A159803 Adjacent sequences:  A030714 A030715 A030716 * A030718 A030719 A030720 KEYWORD nonn,tabf,nice AUTHOR EXTENSIONS More terms from Franklin T. Adams-Watters, Dec 14 2006 STATUS approved

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