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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

Clark Kimberling

EXTENSIONS

More terms from Franklin T. Adams-Watters, Dec 14 2006

STATUS

approved

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Last modified December 5 21:40 EST 2016. Contains 278771 sequences.