

A030717


Table with T(1,1) = 1; for n>1, T(n,k) is the number of k's in rows 1 through n1.


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
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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 k1; state 1 is 1 in row 1.


LINKS

Franklin T. AdamsWatters, 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 !! (n1) !! (k1)
a030717_row n = a030717_tabf !! (n1)
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

Clark Kimberling


EXTENSIONS

More terms from Franklin T. AdamsWatters, Dec 14 2006


STATUS

approved



