|
| |
|
|
A165441
|
|
Table T(k,n) read by antidiagonals: denominator of 1/min(n,k)^2 -1/max(n,k)^2.
|
|
4
|
|
|
|
1, 4, 4, 9, 1, 9, 16, 36, 36, 16, 25, 16, 1, 16, 25, 36, 100, 144, 144, 100, 36, 49, 9, 225, 1, 225, 9, 49, 64, 196, 12, 400, 400, 12, 196, 64, 81, 64, 441, 144, 1, 144, 441, 64, 81, 100, 324, 576, 784, 900, 900, 784, 576, 324, 100, 121, 25, 81, 64, 1225, 1, 1225, 64, 81, 25, 121
(list;
table;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
|
OFFSET
|
1,2
|
|
|
COMMENTS
|
A synopsis of the denominators of the transitions in the Rydberg-Ritz spectrum of hydrogenic atoms.
|
|
|
LINKS
|
Alois P. Heinz, Table of n, a(n) for n = 1..1035
|
|
|
FORMULA
|
T(n,k) = A165727(n,k).
|
|
|
EXAMPLE
|
.1, 4, 9, 16, 25, 36, 49, 64, 81, ... A000290
.4, 1, 36, 16, 100, 9, 196, 64, 324, ... A061038
.9, 36, 1, 144, 225, 12, 441, 576, 81, ... A061040
16, 16, 144, 1, 400, 144, 784, 64, 1296, ... A061042
25, 100, 225, 400, 1, 900, 1225, 1600, 2025, ... A061044
36, 9, 12, 144, 900, 1, 1764, 576, 324, ... A061046
49, 196, 441, 784, 1225, 1764, 1, 3136, 3969, ... A061048
64, 64, 576, 64, 1600, 576, 3136, 1, 5184, ... A061050
81, 324, 81, 1296, 2025, 324, 3969, 5184, 1, ...
|
|
|
MAPLE
|
T:= (k, n)-> denom(1/min (n, k)^2 -1/max (n, k)^2):
seq(seq(T(k, d-k), k=1..d-1), d=2..12);
|
|
|
MATHEMATICA
|
T[n_, k_] := Denominator[1/Min[n, k]^2 - 1/Max[n, k]^2];
Table[T[n-k, k], {n, 2, 12}, {k, 1, n-1}] // Flatten (* Jean-François Alcover, Feb 04 2020 *)
|
|
|
CROSSREFS
|
Sequence in context: A134576 A176441 A143183 * A204997 A178840 A246668
Adjacent sequences: A165438 A165439 A165440 * A165442 A165443 A165444
|
|
|
KEYWORD
|
nonn,tabl,frac,look,easy
|
|
|
AUTHOR
|
Paul Curtz, Sep 19 2009
|
|
|
EXTENSIONS
|
Edited by R. J. Mathar, Feb 27 2010, Mar 03 2010
|
|
|
STATUS
|
approved
|
| |
|
|
