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%I #21 Sep 05 2012 13:31:13
%S 1,3,4,7,8,10,14,16,17,20,25,28,29,31,35,41,45,47,48,51,56,63,68,71,
%T 72,74,78,84,92,98,102,104,105,108,113,120,129,136,141,144,145,147,
%U 151,157,165,175,183,189,193,195,196,199,204,211,220,231
%N 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.
%C Additional comments from _Omar E. Pol_, Sep 02 2012: (Start)
%C Q: What are energy levels?
%C 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
%C Q: What defines the order in A212121?
%C A: The order of A212121 is defined by A212122.
%C Note that there are at least five versions of the nuclear shell model in the OEIS:
%C Goeppert-Mayer (1950): A212012, A004736, A212013, A212014.
%C Goeppert-Mayer, Jensen (1955): A212122, A212121, A212123, A212124.
%C Talmi (1993): A213362, A213361, A213363, A213364.
%C Meyerhof: A213372, A213371, A213373, A213374.
%C For another version: A162630, A130517, A210983, A210984.
%C Each version is represented by four sequences: the first sequence is the main entry.
%C (End)
%C For additional information see A162630.
%F a(n) = A210984(n)/2.
%e Example 1: written as a triangle in which row i is related to the (i-1)st level of nucleus, the sequence begins:
%e 1;
%e 3, 4;
%e 7, 8, 10;
%e 14, 16, 17, 20;
%e 25, 28, 29, 31, 35;
%e 41, 45, 47, 48, 51, 56;
%e 63, 68, 71, 72, 74, 78, 84;
%e 92, 98, 102, 104, 105, 108, 113, 120;
%e 129, 136, 141, 144, 145, 147, 151, 157, 165;
%e 175, 183, 189, 193, 195, 196, 199, 204, 211, 220;
%e ...
%e Column 1 gives positive terms of A004006. Right border gives positives terms of A000292.
%e 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:
%e 1;
%e 3, 4;
%e 7, 8, 10;
%e 14;
%e 16, 17, 20, 25;
%e 28, 29, 31, 35, 41;
%e 45, 47, 48, 51, 56, 63;
%e 68, 71, 72, 74, 78, 84, 92;
%e 98, 102, 104, 105, 108, 113, 120, 129;
%e 136, 141, 144, 145, 147, 151, 157, 165, 175;
%e 183, 189, 193, 195, 196, 199, 204, 211, 220, 231;
%e ...
%Y Partial sums of A130517 (when that sequence is regarded as a flattened triangle). Other versions are A212013, A212123, A213363, A213373.
%Y Cf. A000292, A004006, A162630, A210984
%K nonn,tabf
%O 1,2
%A _Omar E. Pol_, Jul 14 2012
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