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A026791 Triangle in which n-th row lists juxtaposed lexicographically ordered partitions of n; e.g. the partitions of 3 (1+1+1,1+2,3) appear as 1,1,1,1,2,3 in row 3. 11
1, 1, 1, 2, 1, 1, 1, 1, 2, 3, 1, 1, 1, 1, 1, 1, 2, 1, 3, 2, 2, 4, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 3, 1, 2, 2, 1, 4, 2, 3, 5, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 3, 1, 1, 2, 2, 1, 1, 4, 1, 2, 3, 1, 5, 2, 2, 2, 2, 4, 3, 3, 6, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 3, 1, 1, 1, 2, 2, 1, 1, 1, 4, 1, 1, 2, 3, 1, 1, 5 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,4

COMMENTS

Differs from A080576 in a(18): Here, (...,1+3,2+2,4), there (...,2+2,1+3,4).

The representation of the partitions (for fixed n) is as (weakly) increasing lists of parts, the order between individual partitions (for the same n) is lexicographic. [Joerg Arndt, Sep 03 2013]

LINKS

Alois P. Heinz, Rows n = 1..19, flattened

EXAMPLE

First six rows are:

[[1]];

[[1, 1], [2]];

[[1, 1, 1], [1, 2], [3]];

[[1, 1, 1, 1], [1, 1, 2], [1, 3], [2, 2], [4]];

[[1, 1, 1, 1, 1], [1, 1, 1, 2], [1, 1, 3], [1, 2, 2], [1, 4], [2, 3], [5]];

[[1, 1, 1, 1, 1, 1], [1, 1, 1, 1, 2], [1, 1, 1, 3], [1, 1, 2, 2], [1, 1, 4], [1, 2, 3], [1, 5], [2, 2, 2], [2, 4], [3, 3], [6]];

...

From Omar E. Pol, Sep 03 2013: (Start)

Illustration of initial terms:

----------------------------------

.                     Ordered

n  j      Diagram     partition

----------------------------------

.               _

1  1           |_|    1;

.             _ _

2  1         | |_|    1, 1,

2  2         |_ _|    2;

.           _ _ _

3  1       | | |_|    1, 1, 1,

3  2       | |_ _|    1, 2,

3  3       |_ _ _|    3;

.         _ _ _ _

4  1     | | | |_|    1, 1, 1, 1,

4  2     | | |_ _|    1, 1, 2,

4  3     | |_ _ _|    1, 3,

4  4     |   |_ _|    2, 2,

4  5     |_ _ _ _|    4;

...

(End)

MAPLE

T:= proc(n) local b, ll;

      b:= proc(n, l)

            if n=0 then ll:= ll, l[]

          else seq(b(n-i, [l[], i]), i=`if`(l=[], 1, l[-1])..n)

            fi

          end;

      ll:= NULL; b(n, []); ll

    end:

seq(T(n), n=1..8);  # Alois P. Heinz, Jul 16 2011

MATHEMATICA

T[n0_] := Module[{b, ll}, b[n_, l_] := If[n == 0, ll = Join[ll, l], Table[ b[n - i, Append[l, i]], {i, If[l == {}, 1, l[[-1]]], n}]]; ll = {}; b[n0, {}]; ll]; Table[T[n], {n, 1, 8}] // Flatten (* Jean-Fran├žois Alcover, Aug 05 2015, after Alois P. Heinz *)

CROSSREFS

Row lengths are given in A006128.

Partition lengths are in A193173.

Other partition orderings: A036036, A036037, A080576, A080577, A139100, A181087, A181317, A182937, A193073, A211992.

Sequence in context: A104758 A143227 A302247 * A080576 A321744 A322763

Adjacent sequences:  A026788 A026789 A026790 * A026792 A026793 A026794

KEYWORD

nonn,tabf

AUTHOR

Clark Kimberling

STATUS

approved

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Last modified June 17 19:02 EDT 2019. Contains 324198 sequences. (Running on oeis4.)