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%I #22 Oct 11 2022 11:11:31
%S 0,1,1,1,1,3,1,4,0,1,2,6,0,1,1,3,8,1,1,1,0,1,4,12,1,2,1,0,1,0,1,6,16,
%T 2,2,2,0,1,0,1,0,0,0,1,11,19,5,2,2,0,2,0,1,0,0,0,1,0,0,0,1,19,22,8,2,
%U 2,1,2,0,1,0,0,1,1,0,0,0,1,0,0,1,27,28,11,2,2,1,2,0,2,0,0,1,1,0,0,0,1,0,0,2
%N T(1,0)=0 and for n > 1, T(n,k) is the number of k's in rows 1 to n - 1.
%C Construction as in A333867 but starting with a 0 and including a count of 0s at the start of each row. [Edited by _Peter Munn_, Oct 11 2022]
%C See A342585 for a similarly defined sequence that has been analyzed more and has lists of other related sequences. - _Peter Munn_, Oct 08 2022
%H Reinhard Zumkeller, <a href="/A174382/b174382.txt">Rows n = 1..25 of table, flattened</a>
%e 0;
%e 1; # one zero
%e 1,1; # one zero, one one
%e 1,3; # one zero, three ones
%e 1,4,0,1; # one zero, four ones, zero twos, one three
%o (Haskell)
%o import Data.List (sort, group)
%o a174382 n k = a174382_tabf !! (n-1) !! k
%o a174382_row n = a174382_tabf !! (n-1)
%o a174382_tabf = iterate f [0] where
%o f xs = g (xs ++ [0, 0 ..]) [0..] (map head zs) (map length zs)
%o where g _ _ _ [] = []
%o g (u:us) (k:ks) hs'@(h:hs) vs'@(v:vs)
%o | k == h = u + v : g us ks hs vs
%o | k /= h = u : g us ks hs' vs'
%o zs = group $ sort xs
%o -- _Reinhard Zumkeller_, Apr 06 2014
%Y Cf. A240508 (row lengths).
%Y Cf. A333867, A342585.
%K easy,nonn,tabf,look
%O 1,6
%A _Paolo P. Lava_ & _Giorgio Balzarotti_, Mar 17 2010
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