This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A288425 #23 Dec 11 2021 04:30:47 %S A288425 0,1,3,6,10,15,22,30,39,50 %N A288425 Minimal number of vertices that must be selected from an n X n square grid so that any square of 4 vertices, regardless of orientation, will include at least one selected vertex. %C A288425 See the formula and A240443 to deduce lower bounds here: for example, a(11) <= 63, a(12) <= 77. %F A288425 a(n) = n^2 - A240443(n). %e A288425 For n = 3, an extra selection is required compared to A152125 (which considers only squares with sides parallel to the grid), because of the angled square consisting of the midpoints of the edges. One solution (with selected points shown as X) is: %e A288425 X X . %e A288425 . X . %e A288425 . . . %Y A288425 Cf. A240443 (the complementary problem), A152125, A227116. %Y A288425 The number of squares to be considered is A002415. %K A288425 nonn,hard,more %O A288425 1,3 %A A288425 _Ed Wynn_, Jun 09 2017 %E A288425 a(10) derived from A240443(10) by _Hugo van der Sanden_, Nov 04 2021