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.

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

Offset

1,2

Comments

For another version see A213361. First differs from A213361 at a(12).

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

Links

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

Formula

a(n) = A212122(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   |   |   |   |   |   |   |   |   |   |   |
.|   |   |   |   |   |   |   |   |   |   |   4   |   |   |
.|   |   |   |   |   3   |   |   |   |   |   |   |   |   |
.|   |   |   |   |   |   |   |   |   2   |   |   |   |   |
.|   |   |   |   |   |   |   1   |   |   |   |   |   |   |
.|   |   6   |   |   |   |   |   |   |   |   |   |   |   |
.|   |   |   |   |   |   |   |   |   |   |   |   5   |   |
.|   |   |   |   4   |   |   |   |   |   |   |   |   |   |
.|   |   |   |   |   |   |   |   |   |   3   |   |   |   |
.|   |   |   |   |   |   2   |   |   |   |   |   |   |   |
.|   |   |   |   |   |   |   |   1   |   |   |   |   |   |
.|   7   |   |   |   |   |   |   |   |   |   |   |   |   |
.|   |   |   5   |   |   |   |   |   |   |   |   |   |   |
.|   |   |   |   |   3   |   |   |   |   |   |   |   |   |
.|   |   |   |   |   |   |   |   |   |   |   |   |   6   |
.|   |   |   |   |   |   |   |   |   |   |   4   |   |   |
.|   |   |   |   |   |   |   1   |   |   |   |   |   |   |
.|   |   |   |   |   |   |   |   |   2   |   |   |   |   |
.8   |   |   |   |   |   |   |   |   |   |   |   |   |   |
.|   |   |   |   |   |   |   |   |   |   |   |   |   |   |
.|   |   |   |   |   |   |   |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;
4, 3, 2, 1, 6;
5, 4, 3, 2, 1, 7;
5, 3, 6, 4, 1, 2, 8;
...

Crossrefs

Partial sums give A212123.

Cf. A018226, A130517, A212122, A212124, A213361-A213364.

Sequence in context: A130212 A133737 A213361 * A213371 A125047 A323420

Adjacent sequences: A212118 A212119 A212120 * A212122 A212123 A212124

Keyword

nonn,tabf,hard,more

Author

Omar E. Pol, Jun 03 2012

Status

approved