A210983 Total number of pairs of states of the first n subshells of the nuclear shell model in which the subshells are ordered by energy level in increasing order.

1, 3, 4, 7, 8, 10, 14, 16, 17, 20, 25, 28, 29, 31, 35, 41, 45, 47, 48, 51, 56, 63, 68, 71, 72, 74, 78, 84, 92, 98, 102, 104, 105, 108, 113, 120, 129, 136, 141, 144, 145, 147, 151, 157, 165, 175, 183, 189, 193, 195, 196, 199, 204, 211, 220, 231

Offset

1,2

Comments

Additional comments from Omar E. Pol, Sep 02 2012: (Start)

Q: What are energy levels?

A: See the link sections of A212122, A213362, A213372. For example, see this link related to A213372: http://www.flickr.com/photos/mitopencourseware/3772864128/in/set-72157621892931990

Q: What defines the order in A212121?

A: The order of A212121 is defined by A212122.

Note that there are at least five versions of the nuclear shell model in the OEIS:

Goeppert-Mayer (1950): A212012, A004736, A212013, A212014.

Goeppert-Mayer, Jensen (1955): A212122, A212121, A212123, A212124.

Talmi (1993): A213362, A213361, A213363, A213364.

Meyerhof: A213372, A213371, A213373, A213374.

For another version: A162630, A130517, A210983, A210984.

Each version is represented by four sequences: the first sequence is the main entry.

(End)

For additional information see A162630.

Links

Table of n, a(n) for n=1..56.

Formula

a(n) = A210984(n)/2.

Example

Example 1: written as a triangle in which row i is related to the (i-1)st level of nucleus, the sequence begins:
1;
3,     4;
7,     8,  10;
14,   16,  17,  20;
25,   28,  29,  31,  35;
41,   45,  47,  48,  51,  56;
63,   68,  71,  72,  74,  78,  84;
92,   98, 102, 104, 105, 108, 113, 120;
129, 136, 141, 144, 145, 147, 151, 157, 165;
175, 183, 189, 193, 195, 196, 199, 204, 211, 220;
...
Column 1 gives positive terms of A004006. Right border gives positives terms of A000292.
Example 2: written as an irregular triangle in which row j is related to the j-th shell of nucleus. Note that in this case row 4 has only one term. Triangle begins:
1;
3,     4;
7,     8,  10;
14;
16,   17,  20,  25;
28,   29,  31,  35,  41;
45,   47,  48,  51,  56,  63;
68,   71,  72,  74,  78,  84,  92;
98,  102, 104, 105, 108, 113, 120, 129;
136, 141, 144, 145, 147, 151, 157, 165, 175;
183, 189, 193, 195, 196, 199, 204, 211, 220, 231;
...

Crossrefs

Partial sums of A130517 (when that sequence is regarded as a flattened triangle). Other versions are A212013, A212123, A213363, A213373.

Cf. A000292, A004006, A162630, A210984

Sequence in context: A153144 A032788 A338733 * A213363 A212123 A213373

Adjacent sequences: A210980 A210981 A210982 * A210984 A210985 A210986

Keyword

nonn,tabf

Author

Omar E. Pol, Jul 14 2012

Status

approved