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 A212122 #34 Oct 06 2013 13:29:56 %S A212122 2,4,2,6,2,4,8,4,6,2,10,8,6,4,2,12,10,8,6,4,2,14,10,6,12,8,2,4,16 %N A212122 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 A212122 First differs from A213362 at a(12). %C A212122 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), 1g_(7/2), 2d_(5/2), 2d_(3/2), etc. (see link section). The numerators of the fractions are 1, 3, 1, 5, 1, 3, 7, 3, 5, 1, 9, 7, 5, 3,... then we add 1 to every numerator, so we have this sequence: 2, 4, 2, 6, 2, 4, 8, 4, 6, 2, 10, 8, 6, 4,... Other sequences that arise from this sequence are A212121, A212123, A212124. - _Omar E. Pol_, Sep 02 2012 %D A212122 M. Goeppert Mayer and J. Hans D. Jensen, Elementary Theory of Nuclear Shell Structure, J. Wiley and Sons, Inc. (1955). %H A212122 HyperPhysics, G.S.U., <a href="http://hyperphysics.phy-astr.gsu.edu/hbase/nuclear/shell.html">Shell Model of Nucleus</a> %H A212122 Library of Halexandria, <a href="http://www.halexandria.org/dward472.htm">Nuclear shell model</a>, Table 1. %F A212122 a(n) = 2*A212121(n). %e A212122 Illustration of initial terms: two views of a three-dimensional shell model of nucleus. %e A212122 |-------------------------- j --------------------------| %e A212122 | | %e A212122 | |---------------------- i ----------------------| | %e A212122 | | | | %e A212122 | | |------------------ h ------------------| | | %e A212122 | | | | | | %e A212122 | | | |-------------- g --------------| | | | %e A212122 | | | | | | | | %e A212122 | | | | |---------- f ----------| | | | | %e A212122 | | | | | | | | | | %e A212122 | | | | | |------ d ------| | | | | | %e A212122 | | | | | | | | | | | | %e A212122 | | | | | | |-- p --| | | | | | | %e A212122 | | | | | | | | | | | | | | %e A212122 | | | | | | | s | | | | | | | %e A212122 | | | | | | | | | | | | | | | %e A212122 | | | | | | | 2 | | | | | | | %e A212122 | | | | | | 4 | | | | | | | | %e A212122 | | | | | | | | 2 | | | | | | %e A212122 | | | | | 6 | | | | | | | | | %e A212122 | | | | | | | 2 | | | | | | | %e A212122 | | | | | | | | | 4 | | | | | %e A212122 | | | | 8 | | | | | | | | | | %e A212122 | | | | | | 4 | | | | | | | | %e A212122 | | | | | | | | | | 6 | | | | %e A212122 | | | | | | | | 2 | | | | | | %e A212122 | | | 10 | | | | | | | | | | | %e A212122 | | | | | | | | | | | 8 | | | %e A212122 | | | | | 6 | | | | | | | | | %e A212122 | | | | | | | | | 4 | | | | | %e A212122 | | | | | | | 2 | | | | | | | %e A212122 | | 12 | | | | | | | | | | | | %e A212122 | | | | | | | | | | | | 10 | | %e A212122 | | | | 8 | | | | | | | | | | %e A212122 | | | | | | | | | | 6 | | | | %e A212122 | | | | | | 4 | | | | | | | | %e A212122 | | | | | | | | 2 | | | | | | %e A212122 | 14 | | | | | | | | | | | | | %e A212122 | | | 10 | | | | | | | | | | | %e A212122 | | | | | 6 | | | | | | | | | %e A212122 | | | | | | | | | | | | | 12 | %e A212122 | | | | | | | | | | | 8 | | | %e A212122 | | | | | | | 2 | | | | | | | %e A212122 | | | | | | | | | 4 | | | | | %e A212122 16 | | | | | | | | | | | | | | %e A212122 | | | | | | | | | | | | | | | %e A212122 | | | | | | | |1/2| | | | | | | %e A212122 | | | | | | | | | | | | | %e A212122 | | | | | | |----3/2----| | | | | | %e A212122 | | | | | | | | | | | %e A212122 | | | | | |--------5/2--------| | | | | %e A212122 | | | | | | | | | %e A212122 | | | | |------------7/2------------| | | | %e A212122 | | | | | | | %e A212122 | | | |----------------9/2----------------| | | %e A212122 | | | | | %e A212122 | | |-------------------11/2--------------------| | %e A212122 | | | %e A212122 | |-----------------------13/2------------------------| %e A212122 | %e A212122 |---------------------------15/2------------------------- %e A212122 . %e A212122 .......................................................... %e A212122 . %e A212122 |-------------------------- j --------------------------| %e A212122 * | %e A212122 * |---------------------- i ----------------------| | %e A212122 | * | * %e A212122 | * |------------------ h ------------------| | * %e A212122 * | * | * | %e A212122 * | * |-------------- f --------------| | * | %e A212122 | * | * | * | * %e A212122 | * | * |---------- e ----------| | * | * %e A212122 * | * | * | * | * | %e A212122 * | * | * |------ d ------| | * | * | %e A212122 | * | * | * | * | * | * %e A212122 | * | * | * |-- p --| | * | * | * %e A212122 * | * | * | * | * | * | * | %e A212122 * | * | * | * s | * | * | * | %e A212122 | * | * | * | * * | * | * | * %e A212122 | * | * | * | * * | * | * | * %e A212122 * | * | * | * | | * | * | * | %e A212122 * | * | * | * |1/2| * | * | * | %e A212122 | * | * | * | | * | * | * %e A212122 | * | * | * |----3/2----| * | * | * %e A212122 * | * | * | | * | * | %e A212122 * | * | * |--------5/2--------| * | * | %e A212122 | * | * | | * | * %e A212122 | * | * |------------7/2------------| * | * %e A212122 * | * | | * | %e A212122 * | * |----------------9/2----------------| * | %e A212122 | * | | * %e A212122 | * |-------------------11/2--------------------| * %e A212122 * | | %e A212122 * |-----------------------13/2------------------------| %e A212122 | %e A212122 |---------------------------15/2------------------------- %e A212122 . %e A212122 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 A212122 2; %e A212122 4, 2; %e A212122 6, 2, 4; %e A212122 8; %e A212122 4, 6, 2, 10; %e A212122 8, 6, 4, 2, 12; %e A212122 10, 8, 6, 4, 2, 14; %e A212122 10, 6, 12, 8, 2, 4, 16; %e A212122 ... %Y A212122 Row sums give A210842. Partial sums give A212124. %Y A212122 Other versions are A162630, A212012, A213362, A213372. %Y A212122 Cf. A018226, A002378, A130517, A130598, A210842, A212121, A212123. %K A212122 nonn,tabf,hard,more %O A212122 1,1 %A A212122 _Omar E. Pol_, Jun 03 2012