A382310 Array read by ascending antidiagonals: A(n,m) is the squared distance between the roots of the 2nd degree equations z^2 +- n*z + m = 0 on the complex plane.
0, 1, 4, 4, 3, 8, 9, 0, 7, 12, 16, 5, 4, 11, 16, 25, 12, 1, 8, 15, 20, 36, 21, 8, 3, 12, 19, 24, 49, 32, 17, 4, 7, 16, 23, 28, 64, 45, 28, 13, 0, 11, 20, 27, 32, 81, 60, 41, 24, 9, 4, 15, 24, 31, 36, 100, 77, 56, 37, 20, 5, 8, 19, 28, 35, 40, 121, 96, 73, 52, 33, 16, 1, 12, 23, 32, 39, 44
Offset: 0
Examples
The array begins as: 0, 4, 8, 12, 16, 20, 24, 28, 32, 36, 40, 44, ... 1, 3, 7, 11, 15, 19, 23, 27, 31, 35, 39, 43, ... 4, 0, 4, 8, 12, 16, 20, 24, 28, 32, 36, 40, ... 9, 5, 1, 3, 7, 11, 15, 19, 23, 27, 31, 35, ... 16, 12, 8, 4, 0, 4, 8, 12, 16, 20, 24, 28, ... 25, 21, 17, 13, 9, 5, 1, 3, 7, 11, 15, 19, ... ... A(2,0) = 4 since z^2 - 2*z = 0 and z^2 + 2*z = 0 have respectively roots 0, 2, and -2, 0 with squared distance equal to 4; A(1,2) = 7 since z^2 - z + 2 = 0 and z^2 + z + 2 = 0 have respectively roots (1 +- i*sqrt(7))/2 and (-1 +- i*sqrt(7))/2 with squared distance equal to 7, where i denotes the imaginary unit.
Crossrefs
Programs
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Mathematica
A[n_,m_]:=Abs[n^2-4m]; Table[A[n-m,m],{n,0,11},{m,0,n}]//Flatten