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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. 9
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 A292595 A269596

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 September 29 12:15 EDT 2020. Contains 337431 sequences. (Running on oeis4.)