cp's OEIS Frontend

A213361 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 A213361 #13 Jun 25 2012 22:05:13
%S A213361 1,2,1,3,1,2,4,2,3,1,5,3,4,1,2,6,4,2,7,5,1,3,5,6,8,3,1,4,2
%N A213361 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 A213361 For another version see A212121. First differs from A212121 at a(12).
%F A213361 a(n) = A213362(n)/2.
%e A213361 Illustration of initial terms: two views of a three-dimensional shell model of nucleus.
%e A213361 .
%e A213361 .|-------------------------- j --------------------------|
%e A213361 .|                                                       |
%e A213361 .|   |---------------------- i ----------------------|   |
%e A213361 .|   |                                               |   |
%e A213361 .|   |   |------------------ h ------------------|   |   |
%e A213361 .|   |   |                                       |   |   |
%e A213361 .|   |   |   |-------------- g --------------|   |   |   |
%e A213361 .|   |   |   |                               |   |   |   |
%e A213361 .|   |   |   |   |---------- f ----------|   |   |   |   |
%e A213361 .|   |   |   |   |                       |   |   |   |   |
%e A213361 .|   |   |   |   |   |------ d ------|   |   |   |   |   |
%e A213361 .|   |   |   |   |   |               |   |   |   |   |   |
%e A213361 .|   |   |   |   |   |   |-- p --|   |   |   |   |   |   |
%e A213361 .|   |   |   |   |   |   |       |   |   |   |   |   |   |
%e A213361 .|   |   |   |   |   |   |   s   |   |   |   |   |   |   |
%e A213361 .|   |   |   |   |   |   |   |   |   |   |   |   |   |   |
%e A213361 .|   |   |   |   |   |   |   1   |   |   |   |   |   |   |
%e A213361 .|   |   |   |   |   |   2   |   |   |   |   |   |   |   |
%e A213361 .|   |   |   |   |   |   |   |   1   |   |   |   |   |   |
%e A213361 .|   |   |   |   |   3   |   |   |   |   |   |   |   |   |
%e A213361 .|   |   |   |   |   |   |   1   |   |   |   |   |   |   |
%e A213361 .|   |   |   |   |   |   |   |   |   2   |   |   |   |   |
%e A213361 .|   |   |   |   4   |   |   |   |   |   |   |   |   |   |
%e A213361 .|   |   |   |   |   |   2   |   |   |   |   |   |   |   |
%e A213361 .|   |   |   |   |   |   |   |   |   |   3   |   |   |   |
%e A213361 .|   |   |   |   |   |   |   |   1   |   |   |   |   |   |
%e A213361 .|   |   |   5   |   |   |   |   |   |   |   |   |   |   |
%e A213361 .|   |   |   |   |   3   |   |   |   |   |   |   |   |   |
%e A213361 .|   |   |   |   |   |   |   |   |   |   |   4   |   |   |
%e A213361 .|   |   |   |   |   |   |   1   |   |   |   |   |   |   |
%e A213361 .|   |   |   |   |   |   |   |   |   2   |   |   |   |   |
%e A213361 .|   |   6   |   |   |   |   |   |   |   |   |   |   |   |
%e A213361 .|   |   |   |   4   |   |   |   |   |   |   |   |   |   |
%e A213361 .|   |   |   |   |   |   2   |   |   |   |   |   |   |   |
%e A213361 .|   7   |   |   |   |   |   |   |   |   |   |   |   |   |
%e A213361 .|   |   |   |   |   |   |   |   |   |   |   |   5   |   |
%e A213361 .|   |   |   |   |   |   |   |   1   |   |   |   |   |   |
%e A213361 .|   |   |   |   |   |   |   |   |   |   3   |   |   |   |
%e A213361 .|   |   |   5   |   |   |   |   |   |   |   |   |   |   |
%e A213361 .|   |   |   |   |   |   |   |   |   |   |   |   |   6   |
%e A213361 .8   |   |   |   |   |   |   |   |   |   |   |   |   |   |
%e A213361 .|   |   |   |   |   3   |   |   |   |   |   |   |   |   |
%e A213361 .|   |   |   |   |   |   |   1   |   |   |   |   |   |   |
%e A213361 .|   |   |   |   |   |   |   |   |   |   |   4   |   |   |
%e A213361 .|   |   |   |   |   |   |   |   |   2   |   |   |   |   |
%e A213361 .|   |   |   |   |   |   |   |   |   |   |   |   |   |   |
%e A213361 .|   |   |   |   |   |   |   |1/2|   |   |   |   |   |   |
%e A213361 .|   |   |   |   |   |   |           |   |   |   |   |   |
%e A213361 .|   |   |   |   |   |   |----3/2----|   |   |   |   |   |
%e A213361 .|   |   |   |   |   |                   |   |   |   |   |
%e A213361 .|   |   |   |   |   |--------5/2--------|   |   |   |   |
%e A213361 .|   |   |   |   |                           |   |   |   |
%e A213361 .|   |   |   |   |------------7/2------------|   |   |   |
%e A213361 .|   |   |   |                                   |   |   |
%e A213361 .|   |   |   |----------------9/2----------------|   |   |
%e A213361 .|   |   |                                           |   |
%e A213361 .|   |   |-------------------11/2--------------------|   |
%e A213361 .|   |                                                   |
%e A213361 .|   |-----------------------13/2------------------------|
%e A213361 .|
%e A213361 .|---------------------------15/2-------------------------
%e A213361 .
%e A213361 ..........................................................
%e A213361 .
%e A213361 .|-------------------------- j --------------------------|
%e A213361 .|                                                       |
%e A213361 .*   |---------------------- i ----------------------|   |
%e A213361 .|   |                                               |   |
%e A213361 .|   *   |------------------ h ------------------|   |   *
%e A213361 .|   |   |                                       |   |   |
%e A213361 .*   |   *   |-------------- f --------------|   |   *   |
%e A213361 .|   |   |   |                               |   |   |   |
%e A213361 .|   *   |   *   |---------- e ----------|   |   *   |   *
%e A213361 .|   |   |   |   |                       |   |   |   |   |
%e A213361 .*   |   *   |   *   |------ d ------|   |   *   |   *   |
%e A213361 .|   |   |   |   |   |               |   |   |   |   |   |
%e A213361 .|   *   |   *   |   *   |-- p --|   |   *   |   *   |   *
%e A213361 .|   |   |   |   |   |   |       |   |   |   |   |   |   |
%e A213361 .*   |   *   |   *   |   *   s   |   *   |   *   |   *   |
%e A213361 .|   |   |   |   |   |   |   |   |   |   |   |   |   |   |
%e A213361 .|   *   |   *   |   *   |   *   *   |   *   |   *   |   *
%e A213361 .|   |   |   |   |   |   |   |   |   |   |   |   |   |   |
%e A213361 .*   |   *   |   *   |   *   |1/2|   *   |   *   |   *   |
%e A213361 .|   |   |   |   |   |   |           |   |   |   |   |   |
%e A213361 .|   *   |   *   |   *   |----3/2----|   *   |   *   |   *
%e A213361 .|   |   |   |   |   |                   |   |   |   |   |
%e A213361 .*   |   *   |   *   |--------5/2--------|   *   |   *   |
%e A213361 .|   |   |   |   |                           |   |   |   |
%e A213361 .|   *   |   *   |------------7/2------------|   *   |   *
%e A213361 .|   |   |   |                                   |   |   |
%e A213361 .*   |   *   |----------------9/2----------------|   *   |
%e A213361 .|   |   |                                           |   |
%e A213361 .|   *   |-------------------11/2--------------------|   *
%e A213361 .|   |                                                   |
%e A213361 .*   |-----------------------13/2------------------------|
%e A213361 .|
%e A213361 .|---------------------------15/2-------------------------
%e A213361 .
%e A213361 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 A213361 1;
%e A213361 2, 1;
%e A213361 3, 1, 2;
%e A213361 4;
%e A213361 2, 3, 1, 5;
%e A213361 3, 4, 1, 2, 6;
%e A213361 4, 2, 7, 5, 1, 3;
%e A213361 5, 6, 8, 3, 1, 4, 2;
%Y A213361 Partial sums give A213363.
%Y A213361 Cf. A018226, A130517, A212121-A212124, A213362, A213364.
%K A213361 nonn,tabf,hard,more
%O A213361 1,2
%A A213361 _Omar E. Pol_, Jun 23 2012