cp's OEIS Frontend

A211987 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 A211987 #24 Jul 18 2022 22:48:07
%S A211987 1,2,1,1,1,2,1,1,1,3,4,2,2,1,2,1,1,1,1,1,3,1,1,4,1,2,2,1,1,2,1,1,1,1,
%T A211987 1,1,1,3,1,2,3,5,6,3,3,4,2,2,2,2,1,4,1,1,2,2,1,1,1,2,1,1,1,1,1,1,1,1,
%U A211987 1,3,1,1,2,3,1,5,1,1,6,1,3,3,1,4,2,1
%N A211987 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 A211987 In order to construct this sequence we use the following rules:
%C A211987 - Consider the partitions of positive integers.
%C A211987 - For each positive integer its shells must be arranged in a spiral.
%C A211987 - The sequence lists one spiral for each positive integer.
%C A211987 - If the integer j is odd then the last composition listed of each spiral is j.
%C A211987 - If the integer j is even then the first composition listed of each spiral is j.
%C A211987 This sequence represents a three-dimensional structure in which each column contains parts of the same size.
%H A211987 Omar E. Pol, <a href="http://www.polprimos.com/imagenespub/polpa403.jpg">Illustration of the transformation of the partitions of 7 (fig. A) into the rows 30..44 (fig. D)</a>
%e A211987 ----------------------------------------------
%e A211987 .                Expanded        Geometric
%e A211987 Compositions    arrangement        model
%e A211987 ----------------------------------------------
%e A211987 1;                  1;              |*|
%e A211987 ----------------------------------------------
%e A211987 2;                  . 2;            |* *|
%e A211987 1,1;                1,1;            |o|*|
%e A211987 ----------------------------------------------
%e A211987 1,2;              1,. 2;          |*|o o|
%e A211987 1,1,1;            1,1,1;          |*|o|o|
%e A211987 3;                3 . .;          |* * *|
%e A211987 ----------------------------------------------
%e A211987 4,;               . . . 4;        |* * * *|
%e A211987 2,2;              . 2,. 2;        |* *|* *|
%e A211987 1,2,1;            1,. 2,1;        |o|o o|*|
%e A211987 1,1,1,1,;         1,1,1,1;        |o|o|o|*|
%e A211987 3,1;              3 . .,1;        |o o o|*|
%e A211987 ----------------------------------------------
%e A211987 1,4;            1,. . . 4;      |*|o o o o|
%e A211987 1,2,2;          1,. 2,. 2;      |*|o o|o o|
%e A211987 1,1,2,1;        1,1,. 2,1;      |*|o|o o|o|
%e A211987 1,1,1,1,1;      1,1,1,1,1;      |*|o|o|o|o|
%e A211987 1,3,1;          1,3 . .,1;      |*|o o o|o|
%e A211987 2,3;            2 .,3 . .;      |* *|* * *|
%e A211987 5;              5 . . . .;      |* * * * *|
%e A211987 ----------------------------------------------
%e A211987 6;              . . . . . 6;    |* * * * * *|
%e A211987 3,3;            . . 3,. . 3;    |* * *|* * *|
%e A211987 4,2;            . . . 4,. 2;    |* * * *|* *|
%e A211987 2,2,2;          . 2,. 2,. 2;    |* *|* *|* *|
%e A211987 1,4,1;          1,. . . 4,1;    |o|o o o o|*|
%e A211987 1,2,2,1;        1,. 2,. 2,1;    |o|o o|o o|*|
%e A211987 1,1,2,1,1;      1,1,. 2,1,1;    |o|o|o o|o|*|
%e A211987 1,1,1,1,1,1;    1,1,1,1,1,1;    |o|o|o|o|o|*|
%e A211987 1,3,1,1;        1,3 . .,1,1;    |o|o o o|o|*|
%e A211987 2,3,1;          2 .,3 . .,1;    |o o|o o o|*|
%e A211987 5,1;            5 . . . .,1;    |o o o o o|*|
%e A211987 ----------------------------------------------
%e A211987 Note that * is a unitary element of every part of the last section of j.
%Y A211987 Rows sums give A036042, n>=1.
%Y A211987 Mirror of A211988. Other spiral versions are A211985, A211986, A211995-A211998. See also A026792, A211983, A211984, A211989, A211992, A211993, A211994, A211999.
%Y A211987 Cf. A000041, A026905, A135010, A138121, A138137, A138879, A182703, A206437.
%K A211987 nonn,tabf
%O A211987 1,2
%A A211987 _Omar E. Pol_, Aug 18 2012