cp's OEIS Frontend

A211986 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 the arms of a spiral.

%I A211986 #21 Jul 18 2022 22:48:11
%S A211986 1,2,1,1,3,1,1,1,2,1,4,2,2,1,2,1,1,1,1,1,1,3,5,3,2,1,3,1,1,1,1,1,1,1,
%T A211986 2,1,1,2,2,1,4,1,6,3,3,2,4,2,2,2,1,4,1,1,2,2,1,1,1,2,1,1,1,1,1,1,1,1,
%U A211986 1,1,3,1,1,3,2,1,5,7,4,3,5,2,3,2,2,1,5,1,1,3,2,1,1,1,3,1,1,1,1,1,1,1,1,1,1,1,2,1,1,1,1,2,2,1,1,1,4,1,1,2,2,2,1,2,4,1,3,3,1,6,1
%N A211986 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 the arms of a spiral.
%C A211986 In order to construct this sequence we use the following rules:
%C A211986 - Consider the partitions of positive integers.
%C A211986 - For each positive integer its shells must be arranged as the arms of a spiral.
%C A211986 - The sequence lists one spiral for each positive integer.
%C A211986 - If the integer j is odd then the first composition listed of each spiral is j.
%C A211986 - If the integer j is even then we use the same spiral of A211988.
%H A211986 Omar E. Pol, <a href="http://www.polprimos.com/imagenespub/polpa402.jpg">Illustration of the rows 30..44 (figure D)</a>
%e A211986 ----------------------------------------------
%e A211986 .                 Expanded         Geometric
%e A211986 Compositions     arrangement         model
%e A211986 ----------------------------------------------
%e A211986 1;                    1;              |*|
%e A211986 ----------------------------------------------
%e A211986 2;                  2 .;            |* *|
%e A211986 1,1;                1,1;            |*|o|
%e A211986 ----------------------------------------------
%e A211986 3;                  . . 3;          |* * *|
%e A211986 1,1,1;              1,1,1;          |o|o|*|
%e A211986 2,1;                2 .,1;          |o o|*|
%e A211986 ----------------------------------------------
%e A211986 4,;               4 . . .;        |* * * *|
%e A211986 2,2;              2 .,2 .;        |* *|* *|
%e A211986 1,2,1;            1,2 .,1;        |*|o o|o|
%e A211986 1,1,1,1,;         1,1,1,1;        |*|o|o|o|
%e A211986 1,3;              1,. . 3;        |*|o o o|
%e A211986 ----------------------------------------------
%e A211986 5;                . . . . 5;      |* * * * *|
%e A211986 3,2;              . . 3,. 2;      |* * *|* *|
%e A211986 1,3,1;            1,. . 3,1;      |o|o o o|*|
%e A211986 1,1,1,1,1;        1,1,1,1,1;      |o|o|o|o|*|
%e A211986 1,2,1,1;          1,2 .,1,1;      |o|o o|o|*|
%e A211986 2,2,1;            2 .,2 .,1;      |o o|o o|*|
%e A211986 4,1;              4 . . .,1;      |o o o o|*|
%e A211986 ----------------------------------------------
%e A211986 6;              6 . . . . .;    |* * * * * *|
%e A211986 3,3;            3 . .,3 . .;    |* * *|* * *|
%e A211986 2,4;            2 .,4 . . .;    |* *|* * * *|
%e A211986 2,2,2;          2 .,2 .,2 .;    |* *|* *|* *|
%e A211986 1,4,1;          1,4 . . .,1;    |*|o o o o|o|
%e A211986 1,2,2,1;        1,2 .,2 .,1;    |*|o o|o o|o|
%e A211986 1,1,2,1,1;      1,1,2 .,1,1;    |*|o|o o|o|o|
%e A211986 1,1,1,1,1,1;    1,1,1,1,1,1;    |*|o|o|o|o|o|
%e A211986 1,1,3,1;        1,1,. . 3,1;    |*|o|o o o|o|
%e A211986 1,3,2;          1,. . 3,. 2;    |*|o o o|o o|
%e A211986 1,5;            1,. . . . 5;    |*|o o o o o|
%e A211986 ------------------------------------------------
%e A211986 Note that * is a unitary element of every part of the last section of j.
%Y A211986 Rows sums give A036042, n>=1.
%Y A211986 Mirror of A211985. Other spiral versions are A211987, A211988, A211995-A211998. See also A026792, A211983, A211984, A211989, A211992, A211993, A211994, A211999.
%Y A211986 Cf. A000041, A026905, A135010, A138121, A138137, A138879, A182703, A206437.
%K A211986 nonn,tabf
%O A211986 1,2
%A A211986 _Omar E. Pol_, Aug 19 2012