cp's OEIS Frontend

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.

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