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A212014 Total number 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 A212014 #23 Mar 14 2025 19:18:15
%S A212014 2,6,8,14,18,20,28,34,38,40,50,58,64,68,70,82,92,100,106,110,112,126,
%T A212014 138,148,156,162,166,168,184,198,210,220,228,234,238,240,258,274,288,
%U A212014 300,310,318,324,328,330,350,368,384,398,410,420,428,434,438,440,462,482,500,516,530,542,552,560,566,570,572
%N A212014 Total number of states of the first n subshells of the nuclear shell model in which the subshells are ordered by energy level in increasing order.
%D A212014 M. Goeppert Mayer, Nuclear configurations in the spin-orbit coupling model. I. Empirical evidence, Phys. Rev. 78: 16 (1950). II. Theoretical considerations, Phys. Rev. 78: 22 (1950).
%H A212014 Paolo Xausa, <a href="/A212014/b212014.txt">Table of n, a(n) for n = 1..11325</a> (rows 1..150 of triangle, flattened).
%F A212014 a(n) = 2*A212013(n).
%e A212014 Example 1: written as a triangle in which row i is related to the (i-1)st level of nucleus. Triangle begins:
%e A212014     2;
%e A212014     6,   8;
%e A212014    14,  18,  20;
%e A212014    28,  34,  38,  40;
%e A212014    50,  58,  64,  68,  70;
%e A212014    82,  92, 100, 106, 110, 112;
%e A212014   126, 138, 148, 156, 162, 166, 168;
%e A212014   ...
%e A212014 Column 1 gives positive terms of A033547. Right border gives positive terms of A007290.
%e A212014 Example 2: written as an irregular triangle in which row j is related to the j-th shell of nucleus. In this case note that row 4 has only one term. Triangle begins:
%e A212014     2;
%e A212014     6,   8;
%e A212014    14,  18,  20;
%e A212014    28;
%e A212014    34,  38,  40,  50;
%e A212014    58,  64,  68,  70,  82;
%e A212014    92, 100, 106, 110, 112, 126;
%e A212014   138, 148, 156, 162, 166, 168, 184;
%e A212014   ...
%e A212014 First seven terms of right border give the "magic numbers" A018226.
%t A212014 2*Accumulate[Flatten[Range[Range[15], 1, -1]]] (* _Paolo Xausa_, Mar 14 2025 *)
%Y A212014 Partial sums of A212012. Other versions are A210984, A212124, A213364, A213374.
%Y A212014 Cf. A004736, A007290, A033547, A018226, A212013.
%K A212014 nonn,tabl,easy
%O A212014 1,1
%A A212014 _Omar E. Pol_, Jul 15 2012