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A246688 Triangle in which n-th row lists lexicographically ordered increasing lists of parts of all partitions of n into distinct parts. 20
1, 2, 1, 2, 3, 1, 3, 4, 1, 4, 2, 3, 5, 1, 2, 3, 1, 5, 2, 4, 6, 1, 2, 4, 1, 6, 2, 5, 3, 4, 7, 1, 2, 5, 1, 3, 4, 1, 7, 2, 6, 3, 5, 8, 1, 2, 6, 1, 3, 5, 1, 8, 2, 3, 4, 2, 7, 3, 6, 4, 5, 9, 1, 2, 3, 4, 1, 2, 7, 1, 3, 6, 1, 4, 5, 1, 9, 2, 3, 5, 2, 8, 3, 7, 4, 6, 10 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

LINKS

Alois P. Heinz, Rows n = 1..32, flattened

EXAMPLE

Triangle begins:

[1];

[2];

[1,2], [3];

[1,3], [4];

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

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

[1,2,4], [1,6], [2,5], [3,4], [7];

[1,2,5], [1,3,4], [1,7], [2,6], [3,5], [8];

[1,2,6], [1,3,5], [1,8], [2,3,4], [2,7], [3,6], [4,5], [9];

[1,2,3,4], [1,2,7], [1,3,6], [1,4,5], [1,9], [2,3,5], [2,8], [3,7], [4,6], [10];

MAPLE

b:= proc(n, i) b(n, i):= `if`(n=0, [[]], `if`(i>n, [],

      [map(x->[i, x[]], b(n-i, i+1))[], b(n, i+1)[]]))

    end:

T:= n-> map(x-> x[], b(n, 1))[]:

seq(T(n), n=1..12);

CROSSREFS

Row lengths are A015723.

Row sums give A066189.

Last elements of rows are A000027.

Cf. A026791, A026793, A118457, A265146.

Sequence in context: A265146 A325537 A072851 * A103627 A344088 A292595

Adjacent sequences:  A246685 A246686 A246687 * A246689 A246690 A246691

KEYWORD

nonn,tabf

AUTHOR

Alois P. Heinz, Sep 01 2014

STATUS

approved

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Last modified August 11 07:13 EDT 2022. Contains 356046 sequences. (Running on oeis4.)