A120073 - OEIS

%I #20 Apr 25 2023 20:18:57

%S 4,9,36,16,16,144,25,100,225,400,36,9,12,144,900,49,196,441,784,1225,

%T 1764,64,64,576,64,1600,576,3136,81,324,81,1296,2025,324,3969,5184,

%U 100,25,900,400,100,225,4900,1600,8100,121,484,1089,1936,3025,4356,5929,7744,9801,12100

%N Denominator triangle for hydrogen spectrum rationals.

%C The corresponding numerator triangle is A120072.

%C See A120072 and A120070 for more details.

%H G. C. Greubel, <a href="/A120073/b120073.txt">Rows n = 2..50 of the triangle, flattened</a>

%H Wofdieter Lang, <a href="/A120072/a120072.txt">First ten rows, rationals and more</a>.

%F a(m,n) = denominator(r(m,n)) with r(m,n) = 1/n^2 - 1/m^2, m>=2, n=1..m-1.

%e For the rational triangle see W. Lang link.

%e Denominator triangle begins as:

%e     4;

%e     9,  36;

%e    16,  16, 144;

%e    25, 100, 225,  400;

%e    36,   9,  12,  144,  900;

%e    49, 196, 441,  784, 1225, 1764;

%e    64,  64, 576,   64, 1600,  576, 3136;

%e    81, 324,  81, 1296, 2025,  324, 3969, 5184;

%e   100,  25, 900,  400,  100,  225, 4900, 1600, 8100;

%t Table[(1/n^2 - 1/m^2)//Denominator, {m,2,15}, {n,m-1}]//Flatten (* _Jean-François Alcover_, Sep 16 2013 *)

%o (Magma) [Denominator(1/k^2 - 1/n^2): k in [1..n-1], n in [2..18]]; // _G. C. Greubel_, Apr 24 2023

%o (SageMath)

%o def A120073(n,k): return denominator(1/k^2 - 1/n^2)

%o flatten([[A120073(n,k) for k in range(1,n)] for n in range(2,19)]) # _G. C. Greubel_, Apr 24 2023

%Y Row sums give A120075.

%Y Cf. A120070, A120072, A120074, A120076, A120077, A126252.

%K nonn,easy,tabl,frac

%O 2,1

%A _Wolfdieter Lang_, Jul 20 2006