A248141 Table read by rows: n-th row contains all subsets of consecutive numbers of 1..n.

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, 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, 4, 5, 1, 2, 3, 4, 5, 6, 1, 2, 2, 3, 3, 4, 4, 5, 5, 6

Offset: 1

Author

Reinhard Zumkeller, Oct 02 2014

Keywords

• nonn
• tabf

Comments

A000292(n) = length of n-th row, whereas A000217(n) = number of all consecutive subsets of numbers 1..n;

A248147(n,k) = A000040(T(n,k)), 1 <= k <= A000292(n).

Examples

			.  1: 1
.  2: 1,2,1,2
.  3: 1,2,3,1,2,2,3,1,2,3
.  4: 1,2,3,4,1,2,2,3,3,4,1,2,3,2,3,4,1,2,3,4
.  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
rows concatenated from:
.  1: [1]
.  2: [1] [2] [1,2]
.  3: [1] [2] [3] [1,2] [2,3] [1,2,3]
.  4: [1] [2] [3] [4] [1,2] [2,3] [3,4] [1,2,3] [2,3,4] [1,2,3,4]
.  5: [1] [2] [3] [4] [5] [1,2] [2,3] [3,4] [4,5] [1,2,3] [2,3,4] ...
		

Links

• Reinhard Zumkeller, Rows n = 1..20 of triangle, flattened

Crossrefs

Cf. A000292 (row lengths), A000217, A248147.

Programs

Haskell

import Data.List (group)
a248141 n k = a248141_tabf !! (n-1) !! (k-1)
a248141_row n = a248141_tabf !! (n-1)
a248141_tabf = map concat usss where
   usss = iterate f [[1]] where
     f vss = group [1 .. last (last vss) + 1] ++
             map (\ws -> ws ++ [last ws + 1]) vss

Mathematica

Flatten[Table[Flatten[Table[Partition[Range[n],i,1],{i,n}]],{n,6}]] (* Harvey P. Dale, Feb 03 2015 *)