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 A355244 #18 Dec 19 2024 11:56:22 %S A355244 1,1,1,1,2,2,1,3,2,2,1,1,2,2,2,1,1,2,2,2,2,1,6,2,2,2,1,6,2,6,2,2,2,2, %T A355244 2,2,1,1,2,2,2,1,1,2,1,2,1,2,2,2,2,2,2,2,2,2,1,2,2,2,2,6,2,1,2,2,1,3, %U A355244 2,-1,2,2,3,2,1,2,-1,3,2,1,2,2,2,2,6,2,1,2,2,1,2 %N A355244 T(w,h)/2 is the minimum slope >= 1/2 that can be chosen as orientation of a w X h rectangle such that the lower bound for the maximum number of covered grid points A354704(w,d) can be achieved by a suitable translation of the rectangle, where T(w,h) and A354704 are triangles read by rows. T(w,h) = -1 if no slope satisfying this condition exists. %H A355244 Hugo Pfoertner, <a href="/A355244/b355244.txt">Table of n, a(n) for n = 1..210</a>, rows 1..20 of triangle, flattened %H A355244 Hugo Pfoertner, <a href="/A355244/a355244.pdf">Illustrations of T(4,2) = 3, T(7,6) = T(9,6) = T(13,12) = 1</a>. %H A355244 Hugo Pfoertner, <a href="/A355244/a355244_1.pdf">Illustrations of T(12,4) = T(12,11) = -1</a>. %H A355244 Hugo Pfoertner, <a href="/A355244/a355244.gp.txt">PARI program</a> %e A355244 The triangle begins: %e A355244 \ h 1 2 3 4 5 6 7 8 9 10 11 12 13 %e A355244 w \ -------------------------------------- %e A355244 1 | 1; | | | | | | | | | | | | %e A355244 2 | 1, 1; | | | | | | | | | | | %e A355244 3 | 1, 2, 2; | | | | | | | | | | %e A355244 4 | 1, 3, 2, 2; | | | | | | | | | %e A355244 5 | 1, 1, 2, 2, 2; | | | | | | | | %e A355244 6 | 1, 1, 2, 2, 2, 2; | | | | | | | %e A355244 7 | 1, 6, 2, 2, 2, 1, 6; | | | | | | %e A355244 8 | 2, 6, 2, 2, 2, 2, 2, 2; | | | | | %e A355244 9 | 1, 1, 2, 2, 2, 1, 1, 2, 1; | | | | %e A355244 10 | 2, 1, 2, 2, 2, 2, 2, 2, 2, 2; | | | %e A355244 11 | 2, 1, 2, 2, 2, 2, 6, 2, 1, 2, 2; | | %e A355244 12 | 1, 3, 2,-1, 2, 2, 3, 2, 1, 2,-1, 3; | %e A355244 13 | 2, 1, 2, 2, 2, 2, 6, 2, 1, 2, 2, 1, 2 %e A355244 . %e A355244 The first linked illustration shows examples where 2 slopes lead to the same number of covered grid points, where then the smallest multiple of 1/2 is used as a term in the sequence. %e A355244 The second illustration shows the two examples where it is not possible to cover the maximum number of grid points with a rectangle whose side slope is an integer multiple of 1/2. %o A355244 (PARI) /* See Pfoertner link. The program can be used to validate the given terms by calling it successively with the slope parameter k, starting with k = 1/2, 2/2=1, 3/2, (4/2 = 2 already covered by 1/2 via symmetry), 5/2, 6/2=3 for the desired rectangle size w X h, until the number of grid points given by A354704(w,k) is reached for the first time as a result. If the slope parameter is not specified, the program attempts to approximate A354704(w,k) and determine a location of the rectangle that maximizes the free margin between the peripheral grid points and the perimeter of the rectangle. */ %Y A355244 Cf. A354704, A354706. %Y A355244 Cf. A355241 (similar, but with number of covered grid points minimized). %K A355244 tabl,sign %O A355244 1,5 %A A355244 _Hugo Pfoertner_, Jun 29 2022