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A030717
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Table with T(1,1) = 1; for n>1, T(n,k) is the number of k's in rows 1 through n-1.
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14
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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
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OFFSET
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1,3
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COMMENTS
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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.
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LINKS
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Franklin T. Adams-Watters, First 32 rows, flattened
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EXAMPLE
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1;
1;
2;
2, 1;
3, 2;
3, 3, 1;
4, 3, 3;
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PROG
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(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
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CROSSREFS
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Cf. A126027 (row lengths), A006920, A030718 (column numbers).
Cf. A174382.
Cf. A253170 (row sums).
Sequence in context: A074754 A322529 A329949 * A280716 A319444 A071285
Adjacent sequences: A030714 A030715 A030716 * A030718 A030719 A030720
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KEYWORD
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nonn,tabf,nice
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AUTHOR
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Clark Kimberling
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EXTENSIONS
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More terms from Franklin T. Adams-Watters, Dec 14 2006
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STATUS
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approved
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