|
%I #13 Mar 30 2012 18:52:03
%S 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,
%T 100,144,144,100,36,0,0,49,9,225,1,225,9,49,0,0,64,196,12,400,400,12,
%U 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
%N 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.
%C A synopsis of the denominators of the transitions in the Rydberg-Ritz spectrum of hydrogenic atoms.
%H Alois P. Heinz, <a href="/A165727/b165727.txt">Table of n, a(n) for n = 0..1034</a>
%e 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, ... A000004
%e 0, 1, 4, 9, 16, 25, 36, 49, 64, 81, ... A000290
%e 0, 4, 1, 36, 16, 100, 9, 196, 64, 324, ... A061038
%e 0, 9, 36, 1, 144, 225, 12, 441, 576, 81, ... A061040
%e 0, 16, 16, 144, 1, 400, 144, 784, 64, 1296, ... A061042
%e 0, 25, 100, 225, 400, 1, 900, 1225, 1600, 2025, ... A061044
%e 0, 36, 9, 12, 144, 900, 1, 1764, 576, 324, ... A061046
%e 0, 49, 196, 441, 784, 1225, 1764, 1, 3136, 3969, ... A061048
%e 0, 64, 64, 576, 64, 1600, 576, 3136, 1, 5184, ... A061050
%e 0, 81, 324, 81, 1296, 2025, 324, 3969, 5184, 1, ...
%p T:= (k,n)-> `if` (n=0 or k=0, 0, denom (1/min (n,k)^2 -1/max (n, k)^2)):
%p seq (seq (T (k, d-k), k=0..d), d=0..11);
%Y Cf. A165441 (top row and left column removed)
%K nonn,tabl,frac,easy
%O 0,8
%A _Paul Curtz_, Sep 25 2009
%E Edited by _R. J. Mathar_, Feb 27 2010, Mar 03 2010
|
