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A248141 Table read by rows: n-th row contains all subsets of consecutive numbers of 1..n. 3
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 (list; graph; refs; listen; history; text; internal format)
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: A105265 A193360 A061394 * A220694 A136314 A121997

Adjacent sequences:  A248138 A248139 A248140 * A248142 A248143 A248144

KEYWORD

nonn,tabf

AUTHOR

Reinhard Zumkeller, Oct 02 2014

STATUS

approved

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Last modified August 22 12:50 EDT 2017. Contains 290948 sequences.