A165727 Table T(k,n) read by antidiagonals: denominator of 1/min(n,k)^2 -1/max(n,k)^2 with T(0,n) = T(k,0) = 0.

0, 0, 0, 0, 1, 0, 0, 4, 4, 0, 0, 9, 1, 9, 0, 0, 16, 36, 36, 16, 0, 0, 25, 16, 1, 16, 25, 0, 0, 36, 100, 144, 144, 100, 36, 0, 0, 49, 9, 225, 1, 225, 9, 49, 0, 0, 64, 196, 12, 400, 400, 12, 196, 64, 0, 0, 81, 64, 441, 144, 1, 144, 441, 64, 81, 0, 0, 100, 324, 576, 784, 900, 900, 784, 576, 324, 100, 0

Offset

0,8

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 = 0..1034

Example

0,  0,   0,   0,    0,    0,    0,    0,    0,    0, ... A000004
0,  1,   4,   9,   16,   25,   36,   49,   64,   81, ... A000290
0,  4,   1,  36,   16,  100,    9,  196,   64,  324, ... A061038
0,  9,  36,   1,  144,  225,   12,  441,  576,   81, ... A061040
0, 16,  16, 144,    1,  400,  144,  784,   64, 1296, ... A061042
0, 25, 100, 225,  400,    1,  900, 1225, 1600, 2025, ... A061044
0, 36,   9,  12,  144,  900,    1, 1764,  576,  324, ... A061046
0, 49, 196, 441,  784, 1225, 1764,    1, 3136, 3969, ... A061048
0, 64,  64, 576,   64, 1600,  576, 3136,    1, 5184, ... A061050
0, 81, 324,  81, 1296, 2025,  324, 3969, 5184,    1, ...

Maple

T:= (k, n)-> `if` (n=0 or k=0, 0, denom (1/min (n, k)^2 -1/max (n, k)^2)):
seq (seq (T (k, d-k), k=0..d), d=0..11);

Crossrefs

Cf. A165441 (top row and left column removed)

Sequence in context: A216060 A230278 A190113 * A284609 A363174 A290448

Adjacent sequences: A165724 A165725 A165726 * A165728 A165729 A165730

Keyword

nonn,tabl,frac,easy

Author

Paul Curtz, Sep 25 2009

Extensions

Edited by R. J. Mathar, Feb 27 2010, Mar 03 2010

Status

approved