A130517 -id:A130517 - cp's OEIS frontend

A213361 Triangle read by rows in which row n lists the number of pairs of states of the subshells of the n-th shell of the nuclear shell model ordered by energy level in increasing order.

1, 2, 1, 3, 1, 2, 4, 2, 3, 1, 5, 3, 4, 1, 2, 6, 4, 2, 7, 5, 1, 3, 5, 6, 8, 3, 1, 4, 2

Offset: 1

Omar E. Pol, Jun 23 2012

For another version see A212121. First differs from A212121 at a(12).

			Illustration of initial terms: two views of a three-dimensional shell model of nucleus.
.
.|-------------------------- j --------------------------|
.|                                                       |
.|   |---------------------- i ----------------------|   |
.|   |                                               |   |
.|   |   |------------------ h ------------------|   |   |
.|   |   |                                       |   |   |
.|   |   |   |-------------- g --------------|   |   |   |
.|   |   |   |                               |   |   |   |
.|   |   |   |   |---------- f ----------|   |   |   |   |
.|   |   |   |   |                       |   |   |   |   |
.|   |   |   |   |   |------ d ------|   |   |   |   |   |
.|   |   |   |   |   |               |   |   |   |   |   |
.|   |   |   |   |   |   |-- p --|   |   |   |   |   |   |
.|   |   |   |   |   |   |       |   |   |   |   |   |   |
.|   |   |   |   |   |   |   s   |   |   |   |   |   |   |
.|   |   |   |   |   |   |   |   |   |   |   |   |   |   |
.|   |   |   |   |   |   |   1   |   |   |   |   |   |   |
.|   |   |   |   |   |   2   |   |   |   |   |   |   |   |
.|   |   |   |   |   |   |   |   1   |   |   |   |   |   |
.|   |   |   |   |   3   |   |   |   |   |   |   |   |   |
.|   |   |   |   |   |   |   1   |   |   |   |   |   |   |
.|   |   |   |   |   |   |   |   |   2   |   |   |   |   |
.|   |   |   |   4   |   |   |   |   |   |   |   |   |   |
.|   |   |   |   |   |   2   |   |   |   |   |   |   |   |
.|   |   |   |   |   |   |   |   |   |   3   |   |   |   |
.|   |   |   |   |   |   |   |   1   |   |   |   |   |   |
.|   |   |   5   |   |   |   |   |   |   |   |   |   |   |
.|   |   |   |   |   3   |   |   |   |   |   |   |   |   |
.|   |   |   |   |   |   |   |   |   |   |   4   |   |   |
.|   |   |   |   |   |   |   1   |   |   |   |   |   |   |
.|   |   |   |   |   |   |   |   |   2   |   |   |   |   |
.|   |   6   |   |   |   |   |   |   |   |   |   |   |   |
.|   |   |   |   4   |   |   |   |   |   |   |   |   |   |
.|   |   |   |   |   |   2   |   |   |   |   |   |   |   |
.|   7   |   |   |   |   |   |   |   |   |   |   |   |   |
.|   |   |   |   |   |   |   |   |   |   |   |   5   |   |
.|   |   |   |   |   |   |   |   1   |   |   |   |   |   |
.|   |   |   |   |   |   |   |   |   |   3   |   |   |   |
.|   |   |   5   |   |   |   |   |   |   |   |   |   |   |
.|   |   |   |   |   |   |   |   |   |   |   |   |   6   |
.8   |   |   |   |   |   |   |   |   |   |   |   |   |   |
.|   |   |   |   |   3   |   |   |   |   |   |   |   |   |
.|   |   |   |   |   |   |   1   |   |   |   |   |   |   |
.|   |   |   |   |   |   |   |   |   |   |   4   |   |   |
.|   |   |   |   |   |   |   |   |   2   |   |   |   |   |
.|   |   |   |   |   |   |   |   |   |   |   |   |   |   |
.|   |   |   |   |   |   |   |1/2|   |   |   |   |   |   |
.|   |   |   |   |   |   |           |   |   |   |   |   |
.|   |   |   |   |   |   |----3/2----|   |   |   |   |   |
.|   |   |   |   |   |                   |   |   |   |   |
.|   |   |   |   |   |--------5/2--------|   |   |   |   |
.|   |   |   |   |                           |   |   |   |
.|   |   |   |   |------------7/2------------|   |   |   |
.|   |   |   |                                   |   |   |
.|   |   |   |----------------9/2----------------|   |   |
.|   |   |                                           |   |
.|   |   |-------------------11/2--------------------|   |
.|   |                                                   |
.|   |-----------------------13/2------------------------|
.|
.|---------------------------15/2-------------------------
.
..........................................................
.
.|-------------------------- j --------------------------|
.|                                                       |
.*   |---------------------- i ----------------------|   |
.|   |                                               |   |
.|   *   |------------------ h ------------------|   |   *
.|   |   |                                       |   |   |
.*   |   *   |-------------- f --------------|   |   *   |
.|   |   |   |                               |   |   |   |
.|   *   |   *   |---------- e ----------|   |   *   |   *
.|   |   |   |   |                       |   |   |   |   |
.*   |   *   |   *   |------ d ------|   |   *   |   *   |
.|   |   |   |   |   |               |   |   |   |   |   |
.|   *   |   *   |   *   |-- p --|   |   *   |   *   |   *
.|   |   |   |   |   |   |       |   |   |   |   |   |   |
.*   |   *   |   *   |   *   s   |   *   |   *   |   *   |
.|   |   |   |   |   |   |   |   |   |   |   |   |   |   |
.|   *   |   *   |   *   |   *   *   |   *   |   *   |   *
.|   |   |   |   |   |   |   |   |   |   |   |   |   |   |
.*   |   *   |   *   |   *   |1/2|   *   |   *   |   *   |
.|   |   |   |   |   |   |           |   |   |   |   |   |
.|   *   |   *   |   *   |----3/2----|   *   |   *   |   *
.|   |   |   |   |   |                   |   |   |   |   |
.*   |   *   |   *   |--------5/2--------|   *   |   *   |
.|   |   |   |   |                           |   |   |   |
.|   *   |   *   |------------7/2------------|   *   |   *
.|   |   |   |                                   |   |   |
.*   |   *   |----------------9/2----------------|   *   |
.|   |   |                                           |   |
.|   *   |-------------------11/2--------------------|   *
.|   |                                                   |
.*   |-----------------------13/2------------------------|
.|
.|---------------------------15/2-------------------------
.
Written as an irregular triangle in which row n represents the n-th shell of nucleus. Note that row 4 has only one term. Triangle begins:
1;
2, 1;
3, 1, 2;
4;
2, 3, 1, 5;
3, 4, 1, 2, 6;
4, 2, 7, 5, 1, 3;
5, 6, 8, 3, 1, 4, 2;

Partial sums give A213363.

Cf. A018226, A130517, A212121-A212124, A213362, A213364.

a(n) = A213362(n)/2.

A213362 Triangle read by rows in which row n lists the number of states of the subshells of the n-th shell of the nuclear shell model ordered by energy level in increasing order.

Original entry on oeis.org

2, 4, 2, 6, 2, 4, 8, 4, 6, 2, 10, 6, 8, 2, 4, 12, 8, 4, 14, 10, 2, 6, 10, 12, 16, 6, 2, 8, 4

Offset: 1

Omar E. Pol, Jun 23 2012

First differs from A212122 at a(12).

The list of the spin-orbit coupling of this version of the nuclear shell model starts: 1s_(1/2), 1p_(3/2), 1p_(1/2), 1d_(5/2), 2s_(1/2), 1d_(3/2), 1f_(7/2), 2p_(3/2), 1f_(5/2), 2p_(1/2), 1g_(9/2), 2d_(5/2), etc. (see link section). The numerators of the fractions are 1, 3, 1, 5, 1, 3, 7, 3, 5, 1, 9, 5,... then we add 1 to every numerator, so we have this sequence: 2, 4, 2, 6, 2, 4, 8, 4, 6, 2, 10, 6,... Note that in the Talmi's table there is a typo: instead 2f_(1/2) should be 2f_(7/2), see references, page 6. Other sequences that arise from this sequence are A213361, A213363, A213364. - Omar E. Pol, Sep 02 2012

			Illustration of initial terms: two views of a three-dimensional shell model of nucleus.
.
.|-------------------------- j --------------------------|
.|                                                       |
.|   |---------------------- i ----------------------|   |
.|   |                                               |   |
.|   |   |------------------ h ------------------|   |   |
.|   |   |                                       |   |   |
.|   |   |   |-------------- g --------------|   |   |   |
.|   |   |   |                               |   |   |   |
.|   |   |   |   |---------- f ----------|   |   |   |   |
.|   |   |   |   |                       |   |   |   |   |
.|   |   |   |   |   |------ d ------|   |   |   |   |   |
.|   |   |   |   |   |               |   |   |   |   |   |
.|   |   |   |   |   |   |-- p --|   |   |   |   |   |   |
.|   |   |   |   |   |   |       |   |   |   |   |   |   |
.|   |   |   |   |   |   |   s   |   |   |   |   |   |   |
.|   |   |   |   |   |   |   |   |   |   |   |   |   |   |
.|   |   |   |   |   |   |   2   |   |   |   |   |   |   |
.|   |   |   |   |   |   4   |   |   |   |   |   |   |   |
.|   |   |   |   |   |   |   |   2   |   |   |   |   |   |
.|   |   |   |   |   6   |   |   |   |   |   |   |   |   |
.|   |   |   |   |   |   |   2   |   |   |   |   |   |   |
.|   |   |   |   |   |   |   |   |   4   |   |   |   |   |
.|   |   |   |   8   |   |   |   |   |   |   |   |   |   |
.|   |   |   |   |   |   4   |   |   |   |   |   |   |   |
.|   |   |   |   |   |   |   |   |   |   6   |   |   |   |
.|   |   |   |   |   |   |   |   2   |   |   |   |   |   |
.|   |   |  10   |   |   |   |   |   |   |   |   |   |   |
.|   |   |   |   |   6   |   |   |   |   |   |   |   |   |
.|   |   |   |   |   |   |   |   |   |   |   8   |   |   |
.|   |   |   |   |   |   |   2   |   |   |   |   |   |   |
.|   |   |   |   |   |   |   |   |   4   |   |   |   |   |
.|   |  12   |   |   |   |   |   |   |   |   |   |   |   |
.|   |   |   |   8   |   |   |   |   |   |   |   |   |   |
.|   |   |   |   |   |   4   |   |   |   |   |   |   |   |
.|  14   |   |   |   |   |   |   |   |   |   |   |   |   |
.|   |   |   |   |   |   |   |   |   |   |   |  10   |   |
.|   |   |   |   |   |   |   |   2   |   |   |   |   |   |
.|   |   |   |   |   |   |   |   |   |   6   |   |   |   |
.|   |   |  10   |   |   |   |   |   |   |   |   |   |   |
.|   |   |   |   |   |   |   |   |   |   |   |   |  12   |
16   |   |   |   |   |   |   |   |   |   |   |   |   |   |
.|   |   |   |   |   6   |   |   |   |   |   |   |   |   |
.|   |   |   |   |   |   |   2   |   |   |   |   |   |   |
.|   |   |   |   |   |   |   |   |   |   |   8   |   |   |
.|   |   |   |   |   |   |   |   |   4   |   |   |   |   |
.|   |   |   |   |   |   |   |   |   |   |   |   |   |   |
.|   |   |   |   |   |   |   |1/2|   |   |   |   |   |   |
.|   |   |   |   |   |   |           |   |   |   |   |   |
.|   |   |   |   |   |   |----3/2----|   |   |   |   |   |
.|   |   |   |   |   |                   |   |   |   |   |
.|   |   |   |   |   |--------5/2--------|   |   |   |   |
.|   |   |   |   |                           |   |   |   |
.|   |   |   |   |------------7/2------------|   |   |   |
.|   |   |   |                                   |   |   |
.|   |   |   |----------------9/2----------------|   |   |
.|   |   |                                           |   |
.|   |   |-------------------11/2--------------------|   |
.|   |                                                   |
.|   |-----------------------13/2------------------------|
.|
.|---------------------------15/2-------------------------
.
..........................................................
.
.|-------------------------- j --------------------------|
.*                                                       |
.*   |---------------------- i ----------------------|   |
.|   *                                               |   *
.|   *   |------------------ h ------------------|   |   *
.*   |   *                                       |   *   |
.*   |   *   |-------------- f --------------|   |   *   |
.|   *   |   *                               |   *   |   *
.|   *   |   *   |---------- e ----------|   |   *   |   *
.*   |   *   |   *                       |   *   |   *   |
.*   |   *   |   *   |------ d ------|   |   *   |   *   |
.|   *   |   *   |   *               |   *   |   *   |   *
.|   *   |   *   |   *   |-- p --|   |   *   |   *   |   *
.*   |   *   |   *   |   *       |   *   |   *   |   *   |
.*   |   *   |   *   |   *   s   |   *   |   *   |   *   |
.|   *   |   *   |   *   |   *   *   |   *   |   *   |   *
.|   *   |   *   |   *   |   *   *   |   *   |   *   |   *
.*   |   *   |   *   |   *   |   |   *   |   *   |   *   |
.*   |   *   |   *   |   *   |1/2|   *   |   *   |   *   |
.|   *   |   *   |   *   |           |   *   |   *   |   *
.|   *   |   *   |   *   |----3/2----|   *   |   *   |   *
.*   |   *   |   *   |                   |   *   |   *   |
.*   |   *   |   *   |--------5/2--------|   *   |   *   |
.|   *   |   *   |                           |   *   |   *
.|   *   |   *   |------------7/2------------|   *   |   *
.*   |   *   |                                   |   *   |
.*   |   *   |----------------9/2----------------|   *   |
.|   *   |                                           |   *
.|   *   |-------------------11/2--------------------|   *
.*   |                                                   |
.*   |-----------------------13/2------------------------|
.|
.|---------------------------15/2-------------------------
.
Written as an irregular triangle in which row n represents the n-th shell of nucleus. Note that row 4 has only one term. Triangle begins:
2;
4,   2;
6,   2,  4;
8;
4,   6,  2, 10;
6,   8,  2,  4, 12;
8,   4, 14, 10,  2,  6;
10, 12, 16,  6,  2,  8,  4;
...

I. Talmi, Simple Models of Complex Nuclei, Hardwood Academic Publishers (1993).

Wikipedia, Nuclear shell model

Partial sums give A213364. Other versions are A162630, A212012, A212122, A213372.

Cf. A018226, A130517, A213361, A213363.

a(n) = 2*A213361(n).

A162521 Magic numbers A018226 divided by 2.

Original entry on oeis.org

1, 4, 10, 14, 25, 41, 63

Offset: 1

Omar E. Pol, Jul 06 2009

Sequence related to atomic nuclei.

Cf. A018226, A130517, A130556, A130598, A130602, A162522, A162523, A162524, A162525.

A162523 First differences of magic numbers A018226, divided by 2.

Original entry on oeis.org

3, 6, 4, 11, 16, 22

Offset: 1

Omar E. Pol, Jul 06 2009

Sequence related to atomic nucleus.

Cf. A018226, A130517, A130556, A130598, A130602, A162521, A162522, A162524, A162525.

a(n) = A162522(n)/2.

A162524 Partial sums of magic numbers A018226.

Original entry on oeis.org

2, 10, 30, 58, 108, 190, 316

Offset: 1

Omar E. Pol, Jul 06 2009

Sequence related to atomic nuclei.

Cf. A018226, A130517, A130556, A130598, A130602, A162521, A162522, A162523, A162525.

Edited by Omar E. Pol, Jul 16 2009

A162525 Partial sums of magic numbers A018226, divided by 2.

Original entry on oeis.org

1, 5, 15, 29, 54, 95, 158

Offset: 1

Omar E. Pol, Jul 06 2009

Sequence related to atomic nuclei.

Cf. A018226, A130517, A130556, A130598, A130602, A162521, A162522, A162523, A162524.

a(n) = A162524(n)/2.

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.

Original entry on oeis.org

1, 3, 4, 7, 8, 10, 14, 16, 17, 20, 25, 28, 29, 31, 35, 41, 45, 47, 48, 51, 56, 63, 68, 71, 72, 74, 78, 84, 92, 98, 102, 104, 105, 108, 113, 120, 129, 136, 141, 144, 145, 147, 151, 157, 165, 175, 183, 189, 193, 195, 196, 199, 204, 211, 220, 231

Offset: 1

Omar E. Pol, Jul 14 2012

Additional comments from Omar E. Pol, Sep 02 2012: (Start)
Q: What are energy levels?
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
Q: What defines the order in A212121?
A: The order of A212121 is defined by A212122.
Note that there are at least five versions of the nuclear shell model in the OEIS:
Goeppert-Mayer (1950): A212012, A004736, A212013, A212014.
Goeppert-Mayer, Jensen (1955): A212122, A212121, A212123, A212124.
Talmi (1993): A213362, A213361, A213363, A213364.
Meyerhof: A213372, A213371, A213373, A213374.
For another version: A162630, A130517, A210983, A210984.
Each version is represented by four sequences: the first sequence is the main entry.
(End)
For additional information see A162630.

			Example 1: written as a triangle in which row i is related to the (i-1)st level of nucleus, the sequence begins:
1;
3,     4;
7,     8,  10;
14,   16,  17,  20;
25,   28,  29,  31,  35;
41,   45,  47,  48,  51,  56;
63,   68,  71,  72,  74,  78,  84;
92,   98, 102, 104, 105, 108, 113, 120;
129, 136, 141, 144, 145, 147, 151, 157, 165;
175, 183, 189, 193, 195, 196, 199, 204, 211, 220;
...
Column 1 gives positive terms of A004006. Right border gives positives terms of A000292.
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:
1;
3,     4;
7,     8,  10;
14;
16,   17,  20,  25;
28,   29,  31,  35,  41;
45,   47,  48,  51,  56,  63;
68,   71,  72,  74,  78,  84,  92;
98,  102, 104, 105, 108, 113, 120, 129;
136, 141, 144, 145, 147, 151, 157, 165, 175;
183, 189, 193, 195, 196, 199, 204, 211, 220, 231;
...

Partial sums of A130517 (when that sequence is regarded as a flattened triangle). Other versions are A212013, A212123, A213363, A213373.

Cf. A000292, A004006, A162630, A210984

a(n) = A210984(n)/2.

A210984 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.

Original entry on oeis.org

2, 6, 8, 14, 16, 20, 28, 32, 34, 40, 50, 56, 58, 62, 70, 82, 90, 94, 96, 102, 112, 126, 136, 142, 144, 148, 156, 168, 184, 196, 204, 208, 210, 216, 226, 240, 258, 272, 282, 288, 290, 294, 302, 314, 330, 350, 366, 378, 386, 390, 392, 398, 408, 422, 440, 462

Offset: 1

Omar E. Pol, Jul 14 2012

			Example 1: written as a triangle in which row i is related to the (i-1)st level of nucleus the sequence begins:
2;
6,     8;
14,   16,  20;
28,   32,  34,  40;
50,   56,  58,  62,  70;
82,   90,  94,  96, 102, 112;
126, 136, 142, 144, 148, 156, 168;
184, 196, 204, 208, 210, 216, 226, 240;
258, 272, 282, 288, 290, 294, 302, 314, 330;
350, 366, 378, 386, 390, 392, 398, 408, 422, 440;
...
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,   16,  20;
28;
32,   34,  40;  50;
56,   58,  62,  70;  82;
90,   94,  96, 102, 112; 126;
136, 142, 144, 148, 156, 168; 184;
196, 204, 208, 210, 216, 226, 240; 258;
272, 282, 288, 290, 294, 302, 314, 330, 350;
366, 378, 386, 390, 392, 398, 408, 422, 440, 462;
...
First seven terms of right border give the "magic numbers" A018226.

Partial sums of A162630. Other versions are A212014, A212124, A213364, A213374.

Cf. A018226, A033547, A007290, A130517, A210983.

a(n) = 2*A210983(n).

A056951 Triangle whose rows show the result of flipping the first, first two, ... and finally first n coins when starting with the stack (1,2,3,4,...,n) [starting with all heads up, where signs show whether particular coins end up heads or tails].

Original entry on oeis.org

-1, -2, 1, -3, -1, 2, -4, -2, 1, 3, -5, -3, -1, 2, 4, -6, -4, -2, 1, 3, 5, -7, -5, -3, -1, 2, 4, 6, -8, -6, -4, -2, 1, 3, 5, 7, -9, -7, -5, -3, -1, 2, 4, 6, 8, -10, -8, -6, -4, -2, 1, 3, 5, 7, 9, -11, -9, -7, -5, -3, -1, 2, 4, 6, 8, 10, -12, -10, -8, -6, -4, -2, 1, 3, 5, 7, 9, 11, -13, -11, -9, -7, -5, -3, -1, 2, 4, 6, 8, 10, 12, -14, -12, -10

Offset: 1

Henry Bottomley, Sep 05 2000

			Third row is constructed by starting from (1, 2, 3), going to (-1, 2, 3), then going to (-2, 1, 3) and finally going to (-3, -1, 2). Rows are: (-1), (-2, 1), (-3, -1, 2), (-4, -2, 1, 3) etc. as each row is reverse of previous row, with signs changed and -n added as the first term in the row.

A003558 is the number of times the operation needs to be repeated to return to the starting point, taking no account of heads/tails (i.e., signs). A002326 is the number required if heads/tails (i.e., signs) are also required to return to their original position.

Cf. A130517 (unsigned version).

t[n_, 1] := -n; t[n_, n_] := n - 1; t[n_, k_] := 2 * k - n - If[2 * k <= n + 1, 2, 1]; Table[t[n, k], {n, 14}, {k, n}] // Flatten (* Jean-François Alcover, Oct 03 2013 *)

T(n, k) = 2k - n - b with 1 <= k <= n (where b = 2 if 2k <= n + 1, b = 1 otherwise).

A138469 Atomic numbers of p-block elements.

Original entry on oeis.org

5, 6, 7, 8, 9, 10, 13, 14, 15, 16, 17, 18, 31, 32, 33, 34, 35, 36, 49, 50, 51, 52, 53, 54, 81, 82, 83, 84, 85, 86, 113, 114, 115, 116, 117, 118

Offset: 1

Paul Curtz, May 09 2008

6 X 6 square of orbital p filling elements in Mendeleyev-Seaborg or Janet-Tarantola periodic table.
The sequence is considered full if we assume that all elements with 8 shells or more, i.e. of periods 8 and higher in Mendeleev's periodic table, have extremely unstable nuclei (extremely short half-life.)
The atomic numbers of elements in each block are
  s-block: 1,2, 3,4, 11,12, 19,20, 37,38, 55,56, 87,88 for Mendeleev's periodic table (Cf. A160914)
  s-block: 1,2, 3,4, 11,12, 19,20, 37,38, 55,56, 87,88, 119,120 for Janet's periodic table (Cf. A160914)
  p-block: 5..10, 13..18, 31..36, 49..54, 81..86, 113..118 (Cf. A138469)
  d-block: 21..30, 39..48, 71..80, 103..112 (Cf. A199934)
  f-block: 57..70, 89..102 (Cf. A217923)

OEIS Wiki, Periodic table

Cf. A130517, A131603, A167268.
Cf. A160914 Atomic numbers of s-block elements.
Cf. A138469 Atomic numbers of p-block elements.
Cf. A199934 Atomic numbers of d-block elements.
Cf. A217923 Atomic numbers of f-block elements.

Edited by Daniel Forgues, May 15 2011

Ref. to A160914 and A199934 inserted by Jean-François Alcover, Oct 15 2012

cp's OEIS Frontend

A213361 Triangle read by rows in which row n lists the number of pairs of states of the subshells of the n-th shell of the nuclear shell model ordered by energy level in increasing order.

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A213362 Triangle read by rows in which row n lists the number of states of the subshells of the n-th shell of the nuclear shell model ordered by energy level in increasing order.

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A162521 Magic numbers A018226 divided by 2.

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A162523 First differences of magic numbers A018226, divided by 2.

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A162524 Partial sums of magic numbers A018226.

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A162525 Partial sums of magic numbers A018226, divided by 2.

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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.

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A210984 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.

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A056951 Triangle whose rows show the result of flipping the first, first two, ... and finally first n coins when starting with the stack (1,2,3,4,...,n) [starting with all heads up, where signs show whether particular coins end up heads or tails].

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A138469 Atomic numbers of p-block elements.

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