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

1,1

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).

Formula

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

Example

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.

Mathematica

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

Crossrefs

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

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

Sequence in context: A271729 A249624 A104636 * A270050 A137831 A117588

Adjacent sequences: A212011 A212012 A212013 * A212015 A212016 A212017

Keyword

nonn,tabl,easy

Author

Omar E. Pol, Jul 15 2012

Status

approved