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

1,3

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).

Links

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

Example

.  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] ...

Mathematica

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

Prog

(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

Crossrefs

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

Sequence in context: A351468 A193360 A061394 * A220694 A136314 A121997

Adjacent sequences: A248138 A248139 A248140 * A248142 A248143 A248144

Keyword

nonn,tabf

Author

Reinhard Zumkeller, Oct 02 2014

Status

approved