Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).
%I #13 Jun 25 2012 22:05:13
%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
%N 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.
%C For another version see A212121. First differs from A212121 at a(12).
%F a(n) = A213362(n)/2.
%e Illustration of initial terms: two views of a three-dimensional shell model of nucleus.
%e .
%e .|-------------------------- j --------------------------|
%e .| |
%e .| |---------------------- i ----------------------| |
%e .| | | |
%e .| | |------------------ h ------------------| | |
%e .| | | | | |
%e .| | | |-------------- g --------------| | | |
%e .| | | | | | | |
%e .| | | | |---------- f ----------| | | | |
%e .| | | | | | | | | |
%e .| | | | | |------ d ------| | | | | |
%e .| | | | | | | | | | | |
%e .| | | | | | |-- p --| | | | | | |
%e .| | | | | | | | | | | | | |
%e .| | | | | | | s | | | | | | |
%e .| | | | | | | | | | | | | | |
%e .| | | | | | | 1 | | | | | | |
%e .| | | | | | 2 | | | | | | | |
%e .| | | | | | | | 1 | | | | | |
%e .| | | | | 3 | | | | | | | | |
%e .| | | | | | | 1 | | | | | | |
%e .| | | | | | | | | 2 | | | | |
%e .| | | | 4 | | | | | | | | | |
%e .| | | | | | 2 | | | | | | | |
%e .| | | | | | | | | | 3 | | | |
%e .| | | | | | | | 1 | | | | | |
%e .| | | 5 | | | | | | | | | | |
%e .| | | | | 3 | | | | | | | | |
%e .| | | | | | | | | | | 4 | | |
%e .| | | | | | | 1 | | | | | | |
%e .| | | | | | | | | 2 | | | | |
%e .| | 6 | | | | | | | | | | | |
%e .| | | | 4 | | | | | | | | | |
%e .| | | | | | 2 | | | | | | | |
%e .| 7 | | | | | | | | | | | | |
%e .| | | | | | | | | | | | 5 | |
%e .| | | | | | | | 1 | | | | | |
%e .| | | | | | | | | | 3 | | | |
%e .| | | 5 | | | | | | | | | | |
%e .| | | | | | | | | | | | | 6 |
%e .8 | | | | | | | | | | | | | |
%e .| | | | | 3 | | | | | | | | |
%e .| | | | | | | 1 | | | | | | |
%e .| | | | | | | | | | | 4 | | |
%e .| | | | | | | | | 2 | | | | |
%e .| | | | | | | | | | | | | | |
%e .| | | | | | | |1/2| | | | | | |
%e .| | | | | | | | | | | | |
%e .| | | | | | |----3/2----| | | | | |
%e .| | | | | | | | | | |
%e .| | | | | |--------5/2--------| | | | |
%e .| | | | | | | | |
%e .| | | | |------------7/2------------| | | |
%e .| | | | | | |
%e .| | | |----------------9/2----------------| | |
%e .| | | | |
%e .| | |-------------------11/2--------------------| |
%e .| | |
%e .| |-----------------------13/2------------------------|
%e .|
%e .|---------------------------15/2-------------------------
%e .
%e ..........................................................
%e .
%e .|-------------------------- j --------------------------|
%e .| |
%e .* |---------------------- i ----------------------| |
%e .| | | |
%e .| * |------------------ h ------------------| | *
%e .| | | | | |
%e .* | * |-------------- f --------------| | * |
%e .| | | | | | | |
%e .| * | * |---------- e ----------| | * | *
%e .| | | | | | | | | |
%e .* | * | * |------ d ------| | * | * |
%e .| | | | | | | | | | | |
%e .| * | * | * |-- p --| | * | * | *
%e .| | | | | | | | | | | | | |
%e .* | * | * | * s | * | * | * |
%e .| | | | | | | | | | | | | | |
%e .| * | * | * | * * | * | * | *
%e .| | | | | | | | | | | | | | |
%e .* | * | * | * |1/2| * | * | * |
%e .| | | | | | | | | | | | |
%e .| * | * | * |----3/2----| * | * | *
%e .| | | | | | | | | | |
%e .* | * | * |--------5/2--------| * | * |
%e .| | | | | | | | |
%e .| * | * |------------7/2------------| * | *
%e .| | | | | | |
%e .* | * |----------------9/2----------------| * |
%e .| | | | |
%e .| * |-------------------11/2--------------------| *
%e .| | |
%e .* |-----------------------13/2------------------------|
%e .|
%e .|---------------------------15/2-------------------------
%e .
%e 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 1;
%e 2, 1;
%e 3, 1, 2;
%e 4;
%e 2, 3, 1, 5;
%e 3, 4, 1, 2, 6;
%e 4, 2, 7, 5, 1, 3;
%e 5, 6, 8, 3, 1, 4, 2;
%Y Partial sums give A213363.
%Y Cf. A018226, A130517, A212121-A212124, A213362, A213364.
%K nonn,tabf,hard,more
%O 1,2
%A _Omar E. Pol_, Jun 23 2012