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A228531 Triangle read by rows in which row n lists the partitions of n in reverse lexicographic order. 3

%I

%S 1,2,1,1,3,1,2,1,1,1,4,2,2,1,3,1,1,2,1,1,1,1,5,2,3,1,4,1,2,2,1,1,3,1,

%T 1,1,2,1,1,1,1,1,6,3,3,2,4,2,2,2,1,5,1,2,3,1,1,4,1,1,2,2,1,1,1,3,1,1,

%U 1,1,2,1,1,1,1,1,1,7,3,4,2,5,2,2,3,1,6

%N Triangle read by rows in which row n lists the partitions of n in reverse lexicographic order.

%C 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 (list-)reversed lexicographic; see examples. [_Joerg Arndt_, Sep 03 2013]

%C Also compositions in the triangle of A066099 that are in nondecreasing order.

%C The equivalent sequence for compositions (ordered partitions) is A066099.

%C Row n has length A006128(n).

%C Row sums give A066186.

%e Illustration of initial terms:

%e ---------------------------------

%e . Ordered

%e n j Diagram partition

%e ---------------------------------

%e . _

%e 1 1 |_| 1;

%e . _ _

%e 2 1 | _| 2,

%e 2 2 |_|_| 1, 1;

%e . _ _ _

%e 3 1 | _ _| 3,

%e 3 2 | | _| 1, 2,

%e 3 3 |_|_|_| 1, 1, 1;

%e . _ _ _ _

%e 4 1 | _ _| 4,

%e 4 2 | _|_ _| 2, 2,

%e 4 3 | | _ _| 1, 3,

%e 4 4 | | | _| 1, 1, 2,

%e 4 5 |_|_|_|_| 1, 1, 1, 1;

%e .

%e Triangle begins:

%e [1];

%e [2],[1,1];

%e [3],[1,2],[1,1,1];

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

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

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

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

%e ...

%Y Cf. A000041, A066099, A026791, A026792, A211992, A228351.

%K nonn,tabf

%O 1,2

%A _Omar E. Pol_, Aug 30 2013

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Last modified July 21 06:53 EDT 2019. Contains 325192 sequences. (Running on oeis4.)