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
Examples
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;
Formula
a(n) = A213362(n)/2.
Comments