A165441 Table T(k,n) read by antidiagonals: denominator of 1/min(n,k)^2 -1/max(n,k)^2.

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

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: A176441 A363683 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