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A211984 A list of ordered partitions of the positive integers in which the shells of each integer are assembled by their tails.

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%I A211984 #15 Jul 18 2022 22:48:18
%S A211984 1,1,1,2,3,1,1,1,2,1,3,1,1,1,1,1,2,1,1,2,2,4,5,3,2,3,1,1,1,1,1,1,1,2,
%T A211984 1,1,1,2,2,1,4,1,5,1,3,2,1,3,1,1,1,1,1,1,1,1,1,2,1,1,1,1,2,2,1,1,4,1,
%U A211984 1,2,2,2,4,2,3,3,6,7,4,3,5,2,3,2,2,5,1,1,3,2,1,1,3,1,1,1,1,1,1,1,1,1,1,1,2,1,1,1,1,1,2,2,1,1,1,4,1,1,1,3,2,1,1,5,1,1,4,2,1,6,1
%N A211984 A list of ordered partitions of the positive integers in which the shells of each integer are assembled by their tails.
%C A211984 The order of the partitions of the odd integers is the same as A211989. The order of the partitions of the even integers is the same as A211999.
%e A211984 A table of partitions.
%e A211984 --------------------------------------------
%e A211984 .              Expanded       Geometric
%e A211984 Partitions     arrangement    model
%e A211984 --------------------------------------------
%e A211984 1;             1;             |*|
%e A211984 --------------------------------------------
%e A211984 1,1;           1,1;           |o|*|
%e A211984 2;             . 2;           |* *|
%e A211984 --------------------------------------------
%e A211984 3;             . . 3;         |* * *|
%e A211984 1,1,1;         1,1,1;         |o|o|*|
%e A211984 2,1;           . 2,1;         |o o|*|
%e A211984 --------------------------------------------
%e A211984 3,1;           . . 3,1;       |o o o|*|
%e A211984 1,1,1,1;       1,1,1,1;       |o|o|o|*|
%e A211984 2,1,1;         . 2,1,1;       |o o|o|*|
%e A211984 2,2;           . 2,. 2;       |* *|* *|
%e A211984 4;             . . . 4;       |* * * *|
%e A211984 --------------------------------------------
%e A211984 5;             . . . . 5;     |* * * * *|
%e A211984 3,2;           . . 3,. 2;     |* * *|* *|
%e A211984 3,1,1;         . . 3,1,1;     |o o o|o|*|
%e A211984 1,1,1,1,1;     1,1,1,1,1;     |o|o|o|o|*|
%e A211984 2,1,1,1;       . 2,1,1,1;     |o o|o|o|*|
%e A211984 2,2,1;         . 2,. 2,1;     |o o|o o|*|
%e A211984 4,1;           . . . 4,1;     |o o o o|*|
%e A211984 --------------------------------------------
%e A211984 5,1;           . . . . 5,1;   |o o o o o|*|
%e A211984 3,2,1;         . . 3,. 2,1;   |o o o|o o|*|
%e A211984 3,1,1,1;       . . 3,1,1,1;   |o o o|o|o|*|
%e A211984 1,1,1,1,1;     1,1,1,1,1,1;   |o|o|o|o|o|*|
%e A211984 2,1,1,1,1;     . 2,1,1,1,1;   |o o|o|o|o|*|
%e A211984 2,2,1,1;       . 2,. 2,1,1;   |o o|o o|o|*|
%e A211984 4,1,1;         . . . 4,1,1;   |o o o o|o|*|
%e A211984 2,2,2;         . 2,. 2,1,1;   |* *|* *|* *|
%e A211984 4,2;           . . . 4,1,1;   |* * * *|* *|
%e A211984 3,3;           . . 3,. . 3;   |* * *|* * *|
%e A211984 6;             . . . . . 6;   |* * * * * *|
%e A211984 --------------------------------------------
%e A211984 Note that * is a unitary element of every part of the last section of j.
%Y A211984 Rows sums give A036042, n>=1.
%Y A211984 Other versions are A211983, A211989, A211999. See also A026792, A211992-A211994. Spiral arrangements are A211985-A211988, A211995-A211998.
%Y A211984 Cf. A000041, A026905, A135010, A138121, A138137, A138879, A182703, A206437.
%K A211984 nonn,tabf
%O A211984 1,4
%A A211984 _Omar E. Pol_, Aug 19 2012