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.

2, 6, 8, 14, 18, 20, 28, 34, 38, 40, 50, 58, 64, 68, 70, 82, 92, 100, 106, 110, 112, 126, 138, 148, 156, 162, 166, 168, 184, 198, 210, 220, 228, 234, 238, 240, 258, 274, 288, 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

Offset: 1

Author

Omar E. Pol, Jul 15 2012

Keywords

• nonn
• tabl
• easy

Examples

			Example 1: written as a triangle in which row i is related to the (i-1)st level of nucleus. Triangle begins:
    2;
    6,   8;
   14,  18,  20;
   28,  34,  38,  40;
   50,  58,  64,  68,  70;
   82,  92, 100, 106, 110, 112;
  126, 138, 148, 156, 162, 166, 168;
  ...
Column 1 gives positive terms of A033547. Right border gives positive terms of A007290.
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:
    2;
    6,   8;
   14,  18,  20;
   28;
   34,  38,  40,  50;
   58,  64,  68,  70,  82;
   92, 100, 106, 110, 112, 126;
  138, 148, 156, 162, 166, 168, 184;
  ...
First seven terms of right border give the "magic numbers" A018226.
		

References

• 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).

Links

• Paolo Xausa, Table of n, a(n) for n = 1..11325 (rows 1..150 of triangle, flattened).

Crossrefs

Partial sums of A212012. Other versions are A210984, A212124, A213364, A213374.

Cf. A004736, A007290, A033547, A018226, A212013.

Programs

Mathematica

2*Accumulate[Flatten[Range[Range[15], 1, -1]]] (* Paolo Xausa, Mar 14 2025 *)

Formula

a(n) = 2*A212013(n).