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.

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

Offset

1,2

Comments

For another version see A212121. First differs from A212121 at a(12).

Links

Table of n, a(n) for n=1..29.

Formula

a(n) = A213362(n)/2.

Example

Illustration of initial terms: two views of a three-dimensional shell model of nucleus.
.
.|-------------------------- j --------------------------|
.|                                                       |
.|   |---------------------- i ----------------------|   |
.|   |                                               |   |
.|   |   |------------------ h ------------------|   |   |
.|   |   |                                       |   |   |
.|   |   |   |-------------- g --------------|   |   |   |
.|   |   |   |                               |   |   |   |
.|   |   |   |   |---------- f ----------|   |   |   |   |
.|   |   |   |   |                       |   |   |   |   |
.|   |   |   |   |   |------ d ------|   |   |   |   |   |
.|   |   |   |   |   |               |   |   |   |   |   |
.|   |   |   |   |   |   |-- p --|   |   |   |   |   |   |
.|   |   |   |   |   |   |       |   |   |   |   |   |   |
.|   |   |   |   |   |   |   s   |   |   |   |   |   |   |
.|   |   |   |   |   |   |   |   |   |   |   |   |   |   |
.|   |   |   |   |   |   |   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   |   |   |   |   |
.|   |   |   |   |   |   |   |   |   |   |   |   |   |   |
.|   |   |   |   |   |   |   |1/2|   |   |   |   |   |   |
.|   |   |   |   |   |   |           |   |   |   |   |   |
.|   |   |   |   |   |   |----3/2----|   |   |   |   |   |
.|   |   |   |   |   |                   |   |   |   |   |
.|   |   |   |   |   |--------5/2--------|   |   |   |   |
.|   |   |   |   |                           |   |   |   |
.|   |   |   |   |------------7/2------------|   |   |   |
.|   |   |   |                                   |   |   |
.|   |   |   |----------------9/2----------------|   |   |
.|   |   |                                           |   |
.|   |   |-------------------11/2--------------------|   |
.|   |                                                   |
.|   |-----------------------13/2------------------------|
.|
.|---------------------------15/2-------------------------
.
..........................................................
.
.|-------------------------- j --------------------------|
.|                                                       |
.*   |---------------------- i ----------------------|   |
.|   |                                               |   |
.|   *   |------------------ h ------------------|   |   *
.|   |   |                                       |   |   |
.*   |   *   |-------------- f --------------|   |   *   |
.|   |   |   |                               |   |   |   |
.|   *   |   *   |---------- e ----------|   |   *   |   *
.|   |   |   |   |                       |   |   |   |   |
.*   |   *   |   *   |------ d ------|   |   *   |   *   |
.|   |   |   |   |   |               |   |   |   |   |   |
.|   *   |   *   |   *   |-- p --|   |   *   |   *   |   *
.|   |   |   |   |   |   |       |   |   |   |   |   |   |
.*   |   *   |   *   |   *   s   |   *   |   *   |   *   |
.|   |   |   |   |   |   |   |   |   |   |   |   |   |   |
.|   *   |   *   |   *   |   *   *   |   *   |   *   |   *
.|   |   |   |   |   |   |   |   |   |   |   |   |   |   |
.*   |   *   |   *   |   *   |1/2|   *   |   *   |   *   |
.|   |   |   |   |   |   |           |   |   |   |   |   |
.|   *   |   *   |   *   |----3/2----|   *   |   *   |   *
.|   |   |   |   |   |                   |   |   |   |   |
.*   |   *   |   *   |--------5/2--------|   *   |   *   |
.|   |   |   |   |                           |   |   |   |
.|   *   |   *   |------------7/2------------|   *   |   *
.|   |   |   |                                   |   |   |
.*   |   *   |----------------9/2----------------|   *   |
.|   |   |                                           |   |
.|   *   |-------------------11/2--------------------|   *
.|   |                                                   |
.*   |-----------------------13/2------------------------|
.|
.|---------------------------15/2-------------------------
.
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:
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;

Crossrefs

Partial sums give A213363.

Cf. A018226, A130517, A212121-A212124, A213362, A213364.

Sequence in context: A316715 A130212 A133737 * A212121 A213371 A125047

Adjacent sequences: A213358 A213359 A213360 * A213362 A213363 A213364

Keyword

nonn,tabf,hard,more

Author

Omar E. Pol, Jun 23 2012

Status

approved