cp's OEIS Frontend

A211985 A list of certain compositions which arise from the ordered partitions of the positive integers in which the shells of each integer are arranged as a spiral.

%I A211985 #16 Jul 18 2022 22:48:15
%S A211985 1,2,1,1,3,1,1,1,1,2,4,2,2,1,2,1,1,1,1,1,3,1,5,2,3,1,3,1,1,1,1,1,1,1,
%T A211985 1,2,1,1,2,2,1,4,6,3,3,4,2,2,2,2,1,4,1,1,2,2,1,1,1,2,1,1,1,1,1,1,1,1,
%U A211985 1,3,1,1,2,3,1,5,1,7,3,4,2,5,2,2,3,1,5,1,1,2,3,1,1,1,3,1,1,1,1,1,1,1,1,1,1,1,1,2,1,1,1,1,2,2,1,1,1,4,1,1,2,2,2,1,4,2,1,3,3,1,6
%N A211985 A list of certain compositions which arise from the ordered partitions of the positive integers in which the shells of each integer are arranged as a spiral.
%C A211985 In order to construct this sequence we use the following rules:
%C A211985 - Consider the partitions of positive integers.
%C A211985 - For each positive integer its shells must be arranged in a spiral.
%C A211985 - The sequence lists one spiral for each positive integer.
%C A211985 - If the integer j is odd then we use the same spiral of A211995.
%C A211985 - If the integer j is even then the first composition listed of each spiral is j.
%e A211985 --------------------------------------------
%e A211985 .               Expanded        Geometric
%e A211985 Compositions   arrangement        model
%e A211985 --------------------------------------------
%e A211985 1;                 1;             |*|
%e A211985 --------------------------------------------
%e A211985 2;                 . 2;           |* *|
%e A211985 1,1;               1,1;           |o|*|
%e A211985 --------------------------------------------
%e A211985 3;               3 . .;         |* * *|
%e A211985 1,1,1;           1,1,1;         |*|o|o|
%e A211985 1,2;             1,. 2;         |*|o o|
%e A211985 --------------------------------------------
%e A211985 4,;              . . . 4;       |* * * *|
%e A211985 2,2;             . 2,. 2;       |* *|* *|
%e A211985 1,2,1;           1,. 2,1;       |o|o o|*|
%e A211985 1,1,1,1,;        1,1,1,1;       |o|o|o|*|
%e A211985 3,1;             3 . .,1;       |o o o|*|
%e A211985 --------------------------------------------
%e A211985 5;             5 . . . .;     |* * * * *|
%e A211985 2,3;           2 .,3 . .;     |* *|* * *|
%e A211985 1,3,1;         1,3 . .,1;     |*|o o o|o|
%e A211985 1,1,1,1,1;     1,1,1,1,1;     |*|o|o|o|o|
%e A211985 1,1,2,1;       1,1,. 2,1;     |*|o|o o|o|
%e A211985 1,2,2;         1,. 2,. 2;     |*|o o|o o|
%e A211985 1,4;           1,. . . 4;     |*|o o o o|
%e A211985 --------------------------------------------
%e A211985 6;             . . . . . 6;   |* * * * * *|
%e A211985 3,3;           . . 3,. . 3;   |* * *|* * *|
%e A211985 4,2;           . . . 4,. 2;   |* * * *|* *|
%e A211985 2,2,2;         . 2,. 2,. 2;   |* *|* *|* *|
%e A211985 1,4,1;         1,. . . 4,1;   |o|o o o o|*|
%e A211985 1,2,2,1;       1,. 2,. 2,1;   |o|o o|o o|*|
%e A211985 1,1,2,1,1;     1,1,. 2,1,1;   |o|o|o o|o|*|
%e A211985 1,1,1,1,1,1;   1,1,1,1,1,1;   |o|o|o|o|o|*|
%e A211985 1,3,1,1;       1,3 . .,1,1;   |o|o o o|o|*|
%e A211985 2,3,1;         2 .,3 . .,1;   |o o|o o o|*|
%e A211985 5,1;           5 . . . .,1;   |o o o o o|*|
%e A211985 --------------------------------------------
%e A211985 Note that * is a unitary element of every part of the last section of j.
%Y A211985 Rows sums give A036042, n>=1.
%Y A211985 Mirror of A211986. Other spiral versions are A211987, A211988, A211995-A211998. See also A026792, A211983, A211984, A211989, A211992, A211993, A211994, A211999.
%Y A211985 Cf. A000041, A026905, A135010, A138121, A138137, A138879, A182703, A206437.
%K A211985 nonn,tabf
%O A211985 1,2
%A A211985 _Omar E. Pol_, Aug 19 2012