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A333867
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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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8
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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, list 1, where, at stage k>1, write i in list 1 and j in list 2, where i is the number of j's in list 1, for j=1,2,...,m, where m=max number in list 1 from stages 1 to k-1; stage 1 is 1 in list 1.
Nevertheless, this sequence starts each row with the count of 1's, not 0's, whose counts are not recorded in the sequence (cf. A174382, which is also initialized with a 0). - Peter Munn, Oct 11 2022
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LINKS
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Michael De Vlieger, Plot a(w(j) + k - 1) at (j,k) for j = 1..60 and w the sequence of partial sums of A126027, showing a(m) = 0 in black, a(m) = 1 in red, and a(m) > 1 in light blue.
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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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MATHEMATICA
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t = {{1}}; Do[AppendTo[t, BinCounts[#, {1, Max[#] + 1}] &[Flatten[t]]], {30}];
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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
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CROSSREFS
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KEYWORD
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nonn,tabf,nice
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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