cp's OEIS Frontend

A212121 Triangle read by rows in which row n lists the number of pairs of states of the subshells of the n-th shell of the nuclear shell model ordered by energy level in increasing order.

%I A212121 #28 Jul 22 2012 14:08:31
%S A212121 1,2,1,3,1,2,4,2,3,1,5,4,3,2,1,6,5,4,3,2,1,7,5,3,6,4,1,2,8
%N A212121 Triangle read by rows in which row n lists the number of pairs of states of the subshells of the n-th shell of the nuclear shell model ordered by energy level in increasing order.
%C A212121 For another version see A213361. First differs from A213361 at a(12).
%C A212121 What defines this sequence? (This appears to be some sort of permutation of A130517 by shifting columns down or upwards in some randomized way.) - _R. J. Mathar_, Jul 22 2012
%F A212121 a(n) = A212122(n)/2.
%e A212121 Illustration of initial terms: two views of a three-dimensional shell model of nucleus.
%e A212121 .
%e A212121 .|-------------------------- j --------------------------|
%e A212121 .|                                                       |
%e A212121 .|   |---------------------- i ----------------------|   |
%e A212121 .|   |                                               |   |
%e A212121 .|   |   |------------------ h ------------------|   |   |
%e A212121 .|   |   |                                       |   |   |
%e A212121 .|   |   |   |-------------- g --------------|   |   |   |
%e A212121 .|   |   |   |                               |   |   |   |
%e A212121 .|   |   |   |   |---------- f ----------|   |   |   |   |
%e A212121 .|   |   |   |   |                       |   |   |   |   |
%e A212121 .|   |   |   |   |   |------ d ------|   |   |   |   |   |
%e A212121 .|   |   |   |   |   |               |   |   |   |   |   |
%e A212121 .|   |   |   |   |   |   |-- p --|   |   |   |   |   |   |
%e A212121 .|   |   |   |   |   |   |       |   |   |   |   |   |   |
%e A212121 .|   |   |   |   |   |   |   s   |   |   |   |   |   |   |
%e A212121 .|   |   |   |   |   |   |   |   |   |   |   |   |   |   |
%e A212121 .|   |   |   |   |   |   |   1   |   |   |   |   |   |   |
%e A212121 .|   |   |   |   |   |   2   |   |   |   |   |   |   |   |
%e A212121 .|   |   |   |   |   |   |   |   1   |   |   |   |   |   |
%e A212121 .|   |   |   |   |   3   |   |   |   |   |   |   |   |   |
%e A212121 .|   |   |   |   |   |   |   1   |   |   |   |   |   |   |
%e A212121 .|   |   |   |   |   |   |   |   |   2   |   |   |   |   |
%e A212121 .|   |   |   |   4   |   |   |   |   |   |   |   |   |   |
%e A212121 .|   |   |   |   |   |   2   |   |   |   |   |   |   |   |
%e A212121 .|   |   |   |   |   |   |   |   |   |   3   |   |   |   |
%e A212121 .|   |   |   |   |   |   |   |   1   |   |   |   |   |   |
%e A212121 .|   |   |   5   |   |   |   |   |   |   |   |   |   |   |
%e A212121 .|   |   |   |   |   |   |   |   |   |   |   4   |   |   |
%e A212121 .|   |   |   |   |   3   |   |   |   |   |   |   |   |   |
%e A212121 .|   |   |   |   |   |   |   |   |   2   |   |   |   |   |
%e A212121 .|   |   |   |   |   |   |   1   |   |   |   |   |   |   |
%e A212121 .|   |   6   |   |   |   |   |   |   |   |   |   |   |   |
%e A212121 .|   |   |   |   |   |   |   |   |   |   |   |   5   |   |
%e A212121 .|   |   |   |   4   |   |   |   |   |   |   |   |   |   |
%e A212121 .|   |   |   |   |   |   |   |   |   |   3   |   |   |   |
%e A212121 .|   |   |   |   |   |   2   |   |   |   |   |   |   |   |
%e A212121 .|   |   |   |   |   |   |   |   1   |   |   |   |   |   |
%e A212121 .|   7   |   |   |   |   |   |   |   |   |   |   |   |   |
%e A212121 .|   |   |   5   |   |   |   |   |   |   |   |   |   |   |
%e A212121 .|   |   |   |   |   3   |   |   |   |   |   |   |   |   |
%e A212121 .|   |   |   |   |   |   |   |   |   |   |   |   |   6   |
%e A212121 .|   |   |   |   |   |   |   |   |   |   |   4   |   |   |
%e A212121 .|   |   |   |   |   |   |   1   |   |   |   |   |   |   |
%e A212121 .|   |   |   |   |   |   |   |   |   2   |   |   |   |   |
%e A212121 .8   |   |   |   |   |   |   |   |   |   |   |   |   |   |
%e A212121 .|   |   |   |   |   |   |   |   |   |   |   |   |   |   |
%e A212121 .|   |   |   |   |   |   |   |1/2|   |   |   |   |   |   |
%e A212121 .|   |   |   |   |   |   |           |   |   |   |   |   |
%e A212121 .|   |   |   |   |   |   |----3/2----|   |   |   |   |   |
%e A212121 .|   |   |   |   |   |                   |   |   |   |   |
%e A212121 .|   |   |   |   |   |--------5/2--------|   |   |   |   |
%e A212121 .|   |   |   |   |                           |   |   |   |
%e A212121 .|   |   |   |   |------------7/2------------|   |   |   |
%e A212121 .|   |   |   |                                   |   |   |
%e A212121 .|   |   |   |----------------9/2----------------    |   |
%e A212121 .|   |   |                                           |   |
%e A212121 .|   |   |-------------------11/2--------------------|   |
%e A212121 .|   |                                                   |
%e A212121 .|   |-----------------------13/2------------------------|
%e A212121 .|
%e A212121 .|---------------------------15/2-------------------------
%e A212121 .
%e A212121 ..........................................................
%e A212121 .
%e A212121 .|-------------------------- j --------------------------|
%e A212121 .|                                                       |
%e A212121 .*   |---------------------- i ----------------------|   |
%e A212121 .|   |                                               |   |
%e A212121 .|   *   |------------------ h ------------------|   |   *
%e A212121 .|   |   |                                       |   |   |
%e A212121 .*   |   *   |-------------- f --------------|   |   *   |
%e A212121 .|   |   |   |                               |   |   |   |
%e A212121 .|   *   |   *   |---------- e ----------|   |   *   |   *
%e A212121 .|   |   |   |   |                       |   |   |   |   |
%e A212121 .*   |   *   |   *   |------ d ------|   |   *   |   *   |
%e A212121 .|   |   |   |   |   |               |   |   |   |   |   |
%e A212121 .|   *   |   *   |   *   |-- p --|   |   *   |   *   |   *
%e A212121 .|   |   |   |   |   |   |       |   |   |   |   |   |   |
%e A212121 .*   |   *   |   *   |   *   s   |   *   |   *   |   *   |
%e A212121 .|   |   |   |   |   |   |   |   |   |   |   |   |   |   |
%e A212121 .|   *   |   *   |   *   |   *   *   |   *   |   *   |   *
%e A212121 .|   |   |   |   |   |   |   |   |   |   |   |   |   |   |
%e A212121 .*   |   *   |   *   |   *   |1/2|   *   |   *   |   *   |
%e A212121 .|   |   |   |   |   |   |           |   |   |   |   |   |
%e A212121 .|   *   |   *   |   *   |----3/2----|   *   |   *   |   *
%e A212121 .|   |   |   |   |   |                   |   |   |   |   |
%e A212121 .*   |   *   |   *   |--------5/2--------|   *   |   *   |
%e A212121 .|   |   |   |   |                           |   |   |   |
%e A212121 .|   *   |   *   |------------7/2------------|   *   |   *
%e A212121 .|   |   |   |                                   |   |   |
%e A212121 .*   |   *   |----------------9/2----------------|   *   |
%e A212121 .|   |   |                                           |   |
%e A212121 .|   *   |-------------------11/2--------------------|   *
%e A212121 .|   |                                                   |
%e A212121 .*   |-----------------------13/2------------------------|
%e A212121 .|
%e A212121 .|---------------------------15/2-------------------------
%e A212121 .
%e A212121 Written as an irregular triangle in which row n represents the n-th shell of nucleus. Note that row 4 has only one term. Triangle begins:
%e A212121 1;
%e A212121 2, 1;
%e A212121 3, 1, 2;
%e A212121 4;
%e A212121 2, 3, 1, 5;
%e A212121 4, 3, 2, 1, 6;
%e A212121 5, 4, 3, 2, 1, 7;
%e A212121 5, 3, 6, 4, 1, 2, 8;
%e A212121 ...
%Y A212121 Partial sums give A212123.
%Y A212121 Cf. A018226, A130517, A212122, A212124, A213361-A213364.
%K A212121 nonn,tabf,hard,more
%O A212121 1,2
%A A212121 _Omar E. Pol_, Jun 03 2012