This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A213362 #29 Jan 23 2023 09:10:24 %S A213362 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 %N 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. %C A213362 First differs from A212122 at a(12). %C A213362 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 %D A213362 I. Talmi, Simple Models of Complex Nuclei, Hardwood Academic Publishers (1993). %H A213362 Wikipedia, <a href="http://en.wikipedia.org/wiki/Nuclear_shell_model">Nuclear shell model</a> %F A213362 a(n) = 2*A213361(n). %e A213362 Illustration of initial terms: two views of a three-dimensional shell model of nucleus. %e A213362 . %e A213362 .|-------------------------- j --------------------------| %e A213362 .| | %e A213362 .| |---------------------- i ----------------------| | %e A213362 .| | | | %e A213362 .| | |------------------ h ------------------| | | %e A213362 .| | | | | | %e A213362 .| | | |-------------- g --------------| | | | %e A213362 .| | | | | | | | %e A213362 .| | | | |---------- f ----------| | | | | %e A213362 .| | | | | | | | | | %e A213362 .| | | | | |------ d ------| | | | | | %e A213362 .| | | | | | | | | | | | %e A213362 .| | | | | | |-- p --| | | | | | | %e A213362 .| | | | | | | | | | | | | | %e A213362 .| | | | | | | s | | | | | | | %e A213362 .| | | | | | | | | | | | | | | %e A213362 .| | | | | | | 2 | | | | | | | %e A213362 .| | | | | | 4 | | | | | | | | %e A213362 .| | | | | | | | 2 | | | | | | %e A213362 .| | | | | 6 | | | | | | | | | %e A213362 .| | | | | | | 2 | | | | | | | %e A213362 .| | | | | | | | | 4 | | | | | %e A213362 .| | | | 8 | | | | | | | | | | %e A213362 .| | | | | | 4 | | | | | | | | %e A213362 .| | | | | | | | | | 6 | | | | %e A213362 .| | | | | | | | 2 | | | | | | %e A213362 .| | | 10 | | | | | | | | | | | %e A213362 .| | | | | 6 | | | | | | | | | %e A213362 .| | | | | | | | | | | 8 | | | %e A213362 .| | | | | | | 2 | | | | | | | %e A213362 .| | | | | | | | | 4 | | | | | %e A213362 .| | 12 | | | | | | | | | | | | %e A213362 .| | | | 8 | | | | | | | | | | %e A213362 .| | | | | | 4 | | | | | | | | %e A213362 .| 14 | | | | | | | | | | | | | %e A213362 .| | | | | | | | | | | | 10 | | %e A213362 .| | | | | | | | 2 | | | | | | %e A213362 .| | | | | | | | | | 6 | | | | %e A213362 .| | | 10 | | | | | | | | | | | %e A213362 .| | | | | | | | | | | | | 12 | %e A213362 16 | | | | | | | | | | | | | | %e A213362 .| | | | | 6 | | | | | | | | | %e A213362 .| | | | | | | 2 | | | | | | | %e A213362 .| | | | | | | | | | | 8 | | | %e A213362 .| | | | | | | | | 4 | | | | | %e A213362 .| | | | | | | | | | | | | | | %e A213362 .| | | | | | | |1/2| | | | | | | %e A213362 .| | | | | | | | | | | | | %e A213362 .| | | | | | |----3/2----| | | | | | %e A213362 .| | | | | | | | | | | %e A213362 .| | | | | |--------5/2--------| | | | | %e A213362 .| | | | | | | | | %e A213362 .| | | | |------------7/2------------| | | | %e A213362 .| | | | | | | %e A213362 .| | | |----------------9/2----------------| | | %e A213362 .| | | | | %e A213362 .| | |-------------------11/2--------------------| | %e A213362 .| | | %e A213362 .| |-----------------------13/2------------------------| %e A213362 .| %e A213362 .|---------------------------15/2------------------------- %e A213362 . %e A213362 .......................................................... %e A213362 . %e A213362 .|-------------------------- j --------------------------| %e A213362 .* | %e A213362 .* |---------------------- i ----------------------| | %e A213362 .| * | * %e A213362 .| * |------------------ h ------------------| | * %e A213362 .* | * | * | %e A213362 .* | * |-------------- f --------------| | * | %e A213362 .| * | * | * | * %e A213362 .| * | * |---------- e ----------| | * | * %e A213362 .* | * | * | * | * | %e A213362 .* | * | * |------ d ------| | * | * | %e A213362 .| * | * | * | * | * | * %e A213362 .| * | * | * |-- p --| | * | * | * %e A213362 .* | * | * | * | * | * | * | %e A213362 .* | * | * | * s | * | * | * | %e A213362 .| * | * | * | * * | * | * | * %e A213362 .| * | * | * | * * | * | * | * %e A213362 .* | * | * | * | | * | * | * | %e A213362 .* | * | * | * |1/2| * | * | * | %e A213362 .| * | * | * | | * | * | * %e A213362 .| * | * | * |----3/2----| * | * | * %e A213362 .* | * | * | | * | * | %e A213362 .* | * | * |--------5/2--------| * | * | %e A213362 .| * | * | | * | * %e A213362 .| * | * |------------7/2------------| * | * %e A213362 .* | * | | * | %e A213362 .* | * |----------------9/2----------------| * | %e A213362 .| * | | * %e A213362 .| * |-------------------11/2--------------------| * %e A213362 .* | | %e A213362 .* |-----------------------13/2------------------------| %e A213362 .| %e A213362 .|---------------------------15/2------------------------- %e A213362 . %e A213362 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: %e A213362 2; %e A213362 4, 2; %e A213362 6, 2, 4; %e A213362 8; %e A213362 4, 6, 2, 10; %e A213362 6, 8, 2, 4, 12; %e A213362 8, 4, 14, 10, 2, 6; %e A213362 10, 12, 16, 6, 2, 8, 4; %e A213362 ... %Y A213362 Partial sums give A213364. Other versions are A162630, A212012, A212122, A213372. %Y A213362 Cf. A018226, A130517, A213361, A213363. %K A213362 nonn,tabf,hard,more %O A213362 1,1 %A A213362 _Omar E. Pol_, Jun 23 2012