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A026792 List of juxtaposed reverse-lexicographically ordered partitions of the positive integers. 23

%I

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

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

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

%N List of juxtaposed reverse-lexicographically ordered partitions of the positive integers.

%C The representation of the partitions (for fixed n) is as (weakly) decreasing lists of parts, the order between individual partitions (for the same n) is (list-)reversed lexicographic; see examples. [_Joerg Arndt_, Sep 03 2013]

%C Written as a triangle; row n has length A006128(n); row sums give A066186. Also written as an irregular tetrahedron in which T(n,j,k) is the k-th largest part of the j-th partition of n; the sum of column k in the slice n is A181187(n,k); right border of the slices gives A182715. - _Omar E. Pol_, Mar 25 2012

%C The equivalent sequence for compositions (ordered partitions) is A228351). - _Omar E. Pol_, Sep 03 2013

%e E.g. the partitions of 3 (3,2+1,1+1+1) appear as the string 3,2,1,1,1,1.

%e So the list begins:

%e 1

%e 2, 1, 1,

%e 3, 2, 1, 1, 1, 1,

%e 4, 2, 2, 3, 1, 2, 1, 1, 1, 1, 1, 1,

%e 5, 3, 2, 4, 1, 2, 2, 1, 3, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1,

%e ...

%e From _Omar E. Pol_, Sep 03 2013: (Start)

%e Illustration of initial terms:

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

%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 |_ | | 2, 1,

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

%e . _ _ _ _

%e 4 1 |_ _ | 4,

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

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

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

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

%e ...

%e (End)

%Y Cf. A026791, A211992, A228351, A228531.

%K nonn,tabf

%O 1,2

%A _Clark Kimberling_

%E Terms 81st, 83rd and 84th corrected by _Omar E. Pol_, Aug 16 2009

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Last modified June 17 04:26 EDT 2019. Contains 324183 sequences. (Running on oeis4.)