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%I #14 Jul 18 2022 22:47:25
%S 1,1,1,2,3,2,1,1,1,1,1,1,1,1,2,1,1,3,1,2,2,4,5,3,2,4,1,2,2,1,3,1,1,2,
%T 1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,1,1,1,1,3,1,1,1,2,2,1,1,4,1,1,3,2,1,5,
%U 1,2,2,2,4,2,3,3,6,7,4,3,5,2,3,2,2,6,1,3,3,1,4,2,1,2,2,2,1,5,1,1,3,2,1,1,4,1,1,1,2,2,1,1,1,3,1,1,1,1,2,1,1,1,1,1,1,1,1,1,1,1,1
%N A list of ordered partitions of the positive integers.
%C The order of the partitions of the odd integers is the same as A026792. The order of the partitions of the even integers is the same as A211992.
%e A table of partitions.
%e --------------------------------------------
%e . Expanded Geometric
%e Partitions arrangement model
%e --------------------------------------------
%e 1; 1; |*|
%e --------------------------------------------
%e 1,1; 1,1; |o|*|
%e 2; . 2; |* *|
%e --------------------------------------------
%e 3; . . 3; |* * *|
%e 2,1; . 2,1; |o o|*|
%e 1,1,1; 1,1,1; |o|o|*|
%e --------------------------------------------
%e 1,1,1,1; 1,1,1,1; |o|o|o|*|
%e 2,1,1; . 2,1,1; |o o|o|*|
%e 3,1; . . 3,1; |o o o|*|
%e 2,2; . 2,. 2; |* *|* *|
%e 4; . . . 4; |* * * *|
%e --------------------------------------------
%e 5; . . . . 5; |* * * * *|
%e 3,2; . . 3,. 2; |* * *|* *|
%e 4,1; . . . 4,1; |o o o o|*|
%e 2,2,1; . 2,. 2,1; |o o|o o|*|
%e 3,1,1; . . 3,1,1; |o o o|o|*|
%e 2,1,1,1; . 2,1,1,1; |o o|o|o|*|
%e 1,1,1,1,1; 1,1,1,1,1; |o|o|o|o|*|
%e --------------------------------------------
%e 1,1,1,1,1,1; 1,1,1,1,1,1; |o|o|o|o|o|*|
%e 2,1,1,1,1; . 2,1,1,1,1; |o o|o|o|o|*|
%e 3,1,1,1; . . 3,1,1,1; |o o o|o|o|*|
%e 2,2,1,1; . 2,. 2,1,1; |o o|o o|o|*|
%e 4,1,1; . . . 4,1,1; |o o o o|o|*|
%e 3,2,1; . . 3,. 2,1; |o o o|o o|*|
%e 5,1; . . . . 5,1; |o o o o o|*|
%e 2,2,2; . 2,. 2,. 2; |* *|* *|* *|
%e 4,2; . . . 4,. 2; |* * * *|* *|
%e 3,3; . . 3,. . 3; |* * *|* * *|
%e 6; . . . . . 6; |* * * * * *|
%e --------------------------------------------
%e Note that * is a unitary element of every part of the last section of j.
%Y Rows sums give A036042, n>=1.
%Y Other versions are A026792, A211992, A211993. See also A211983, A211984, A211989, A211999. Spiral arrangements are A211985-A211988, A211995-A211998.
%Y Cf. A000041, A026905, A135010, A138121, A138137, A138879, A182703, A206437.
%K nonn,tabf
%O 1,4
%A _Omar E. Pol_, Aug 18 2012
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