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A212012
Triangle read by rows in which row n lists the number of states of the subshells of the n-th shell of the nuclear shell model ordered by energy level in increasing order.
8
2, 4, 2, 6, 4, 2, 8, 6, 4, 2, 10, 8, 6, 4, 2, 12, 10, 8, 6, 4, 2, 14, 12, 10, 8, 6, 4, 2, 16, 14, 12, 10, 8, 6, 4, 2, 18, 16, 14, 12, 10, 8, 6, 4, 2, 20, 18, 16, 14, 12, 10, 8, 6, 4, 2, 22, 20, 18, 16, 14, 12, 10, 8, 6, 4, 2, 24, 22, 20, 18, 16, 14, 12
OFFSET
1,1
COMMENTS
Also triangle read by rows in which row i lists the first i positive even numbers in decreasing order.
The list of the spin-orbit coupling of this version of the nuclear shell model starts: 1s_(1/2), 1p_(3/2), 1p_(1/2), 1d_(5/2), 1d_(3/2), etc. (see link section). The numerators of the fractions are 1, 3, 1, 5, 3,... then we add 1 to every numerator, so we have this sequence: 2, 4, 2, 6, 4,... Other sequences that arise from this sequence are both A212013 and A212014. - Omar E. Pol, Sep 02 2012
FORMULA
a(n) = 2*A004736(n).
EXAMPLE
Illustration of initial terms: one of the views of a three-dimensional shell model of nucleus.
.
.|-------------------------- j --------------------------|
.| |
.| |---------------------- i ----------------------| |
.| | | |
.| | |------------------ h ------------------| | |
.| | | | | |
.| | | |-------------- g --------------| | | |
.| | | | | | | |
.| | | | |---------- f ----------| | | | |
.| | | | | | | | | |
.| | | | | |------ d ------| | | | | |
.| | | | | | | | | | | |
.| | | | | | |-- p --| | | | | | |
.| | | | | | | | | | | | | |
.| | | | | | | s | | | | | | |
.| | | | | | | | | | | | | | |
.| | | | | | | 2 | | | | | | |
.| | | | | | 4 | | | | | | | |
.| | | | | | | | 2 | | | | | |
.| | | | | 6 | | | | | | | | |
.| | | | | | | | | 4 | | | | |
.| | | | | | | 2 | | | | | | |
.| | | | 8 | | | | | | | | | |
.| | | | | | | | | | 6 | | | |
.| | | | | | 4 | | | | | | | |
.| | | | | | | | 2 | | | | | |
.| | | 10 | | | | | | | | | | |
.| | | | | | | | | | | 8 | | |
.| | | | | 6 | | | | | | | | |
.| | | | | | | | | 4 | | | | |
.| | | | | | | 2 | | | | | | |
.| | 12 | | | | | | | | | | | |
.| | | | | | | | | | | | 10 | |
.| | | | 8 | | | | | | | | | |
.| | | | | | | | | | 6 | | | |
.| | | | | | 4 | | | | | | | |
.| | | | | | | | 2 | | | | | |
.| 14 | | | | | | | | | | | | |
.| | | | | | | | | | | | | 12 |
.| | | 10 | | | | | | | | | | |
.| | | | | | | | | | | 8 | | |
.| | | | | 6 | | | | | | | | |
.| | | | | | | | | 4 | | | | |
.| | | | | | | 2 | | | | | | |
.| | | | | | | | | | | | | | |
.| | | | | | | | | | | | | | |
.| | | | | | | |1/2| | | | | | |
.| | | | | | | | | | | | |
.| | | | | | |----3/2----| | | | | |
.| | | | | | | | | | |
.| | | | | |--------5/2--------| | | | |
.| | | | | | | | |
.| | | | |------------7/2------------| | | |
.| | | | | | |
.| | | |----------------9/2----------------| | |
.| | | | |
.| | |-------------------11/2--------------------| |
.| | |
.| |-----------------------13/2------------------------|
.|
.|---------------------------15/2-------------------------
.
For another view of the model see the example section of A212122, second part.
Example 1. Triangle begins:
2;
4, 2;
6, 4, 2;
8, 6, 4, 2;
10, 8, 6, 4, 2;
12, 10, 8, 6, 4, 2;
14, 12, 10, 8, 6, 4, 2;
16, 14, 12, 10, 8, 6, 4, 2;
...
Column 1 gives positive terms of A005843. Right border give positive terms of A007395. Row sums give A002378.
Example 2. Written as an irregular triangle in which row j represents the j-th shell of nucleus. Note that row 4 has only one term. Triangle begins:
2;
4, 2;
6, 4, 2;
8;
6, 4, 2, 10;
8, 6, 4, 2, 12;
10, 8, 6, 4, 2, 14;
12, 10, 8, 6, 4, 2, 16;
14, 12, 10, 8, 6, 4, 2, 18;
CROSSREFS
Partial sums give A212014. Other versions are A162630, A212122, A213362, A213372.
Sequence in context: A323307 A215841 A272327 * A322071 A176342 A374456
KEYWORD
nonn,tabf,easy
AUTHOR
Omar E. Pol, Jul 15 2012
STATUS
approved