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

Author

Paul Curtz, Sep 25 2009

Keywords

• nonn
• tabl
• frac
• easy

Comments

A synopsis of the denominators of the transitions in the Rydberg-Ritz spectrum of hydrogenic atoms.

Examples

			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, ...
		

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..1034

Crossrefs

Cf. A165441 (top row and left column removed)

Programs

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);

Extensions

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