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%I #12 Feb 03 2015 17:16:47
%S 1,1,2,1,2,1,2,3,1,2,2,3,1,2,3,1,2,3,4,1,2,2,3,3,4,1,2,3,2,3,4,1,2,3,
%T 4,1,2,3,4,5,1,2,2,3,3,4,4,5,1,2,3,2,3,4,3,4,5,1,2,3,4,2,3,4,5,1,2,3,
%U 4,5,1,2,3,4,5,6,1,2,2,3,3,4,4,5,5,6
%N Table read by rows: n-th row contains all subsets of consecutive numbers of 1..n.
%C A000292(n) = length of n-th row, whereas A000217(n) = number of all consecutive subsets of numbers 1..n;
%C A248147(n,k) = A000040(T(n,k)), 1 <= k <= A000292(n).
%H Reinhard Zumkeller, <a href="/A248141/b248141.txt">Rows n = 1..20 of triangle, flattened</a>
%e . 1: 1
%e . 2: 1,2,1,2
%e . 3: 1,2,3,1,2,2,3,1,2,3
%e . 4: 1,2,3,4,1,2,2,3,3,4,1,2,3,2,3,4,1,2,3,4
%e . 5: 1,2,3,4,5,1,2,2,3,3,4,4,5,1,2,3,2,3,4,3,4,5,1,2,3,4,2,3,4,5,1,2,3,4,5
%e rows concatenated from:
%e . 1: [1]
%e . 2: [1] [2] [1,2]
%e . 3: [1] [2] [3] [1,2] [2,3] [1,2,3]
%e . 4: [1] [2] [3] [4] [1,2] [2,3] [3,4] [1,2,3] [2,3,4] [1,2,3,4]
%e . 5: [1] [2] [3] [4] [5] [1,2] [2,3] [3,4] [4,5] [1,2,3] [2,3,4] ...
%t Flatten[Table[Flatten[Table[Partition[Range[n],i,1],{i,n}]],{n,6}]] (* _Harvey P. Dale_, Feb 03 2015 *)
%o (Haskell)
%o import Data.List (group)
%o a248141 n k = a248141_tabf !! (n-1) !! (k-1)
%o a248141_row n = a248141_tabf !! (n-1)
%o a248141_tabf = map concat usss where
%o usss = iterate f [[1]] where
%o f vss = group [1 .. last (last vss) + 1] ++
%o map (\ws -> ws ++ [last ws + 1]) vss
%Y Cf. A000292 (row lengths), A000217, A248147.
%K nonn,tabf
%O 1,3
%A _Reinhard Zumkeller_, Oct 02 2014
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