A092275 - OEIS

A092275

Draw a line through every pair of points with coordinates (x, 1) and (x', 2) with x, x' in 1..n, and then count the number of intersection points above the line y = 2.

%I #11 Jan 18 2024 09:58:10

%S 0,2,11,29,69,125,224,361,563,809,1164,1597,2188,2871,3714,4701,5956,

%T 7359,9099,11067,13365,15879,18884,22201,26056,30219,34951,40117,

%U 46073,52441,59716,67599,76320,85569,95790,106701,118902

%N Draw a line through every pair of points with coordinates (x, 1) and (x', 2) with x, x' in 1..n, and then count the number of intersection points above the line y = 2.

%H Joseph O'Rourke, <a href="https://www.science.smith.edu/~jorourke/books/ArtGalleryTheorems/art.html">Art Gallery Theorems and Algorithms</a>, Oxford Univ. Press, 1987. See section 8.6, p. 223.

%F a(n) = (A347750(n+1) - A331755(n)) / 2. - _Andrey Zabolotskiy_, Jan 17 2024

%Y Cf. A331755, A347750.

%K nonn

%O 2,2

%A _N. J. A. Sloane_, Feb 17 2004

%E New name and terms a(10) and beyond (using the formula) added by _Andrey Zabolotskiy_, Jan 18 2024