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 A354703 #17 Jul 03 2022 16:24:40 %S A354703 1,1,2,1,2,2,2,3,3,4,2,3,2,3,4,2,4,3,4,4,4,3,5,3,6,4,6,9,3,5,4,5,4,4, %T A354703 7,7,3,6,3,6,4,6,9,6,9,3,6,4,5,4,5,7,6,6,4,4,7,5,7,5,6,10,7,9,5,9,4,8, %U A354703 5,8,5,8,12,8,12,8,12,16,4,8,5,7,4,6,10,6,9,4,8,12,7 %N A354703 T(w,h) = w*h - A354702(w,h) is a lower bound on the gain in the number of not covered grid points from an optimally positioned and rotated cover versus a just translated cover, where T(w,h) and A354702 are triangles read by rows. %H A354703 Hugo Pfoertner, <a href="/A354703/b354703.txt">Table of n, a(n) for n = 1..210</a>, rows 1..20 of triangle, flattened %e A354703 The triangle begins: %e A354703 \ h 1 2 3 4 5 6 7 8 9 10 11 12 13 %e A354703 w \ ------------------------------------------ %e A354703 1 | 1; | | | | | | | | | | | | %e A354703 2 | 1, 2; | | | | | | | | | | | %e A354703 3 | 1, 2, 2; | | | | | | | | | | %e A354703 4 | 2, 3, 3, 4; | | | | | | | | | %e A354703 5 | 2, 3, 2, 3, 4; | | | | | | | | %e A354703 6 | 2, 4, 3, 4, 4, 4; | | | | | | | %e A354703 7 | 3, 5, 3, 6, 4, 6, 9; | | | | | | %e A354703 8 | 3, 5, 4, 5, 4, 4, 7, 7; | | | | | %e A354703 9 | 3, 6, 3, 6, 4, 6, 9, 6, 9; | | | | %e A354703 10 | 3, 6, 4, 5, 4, 5, 7, 6, 6, 4; | | | %e A354703 11 | 4, 7, 5, 7, 5, 6, 10, 7, 9, 5, 9; | | %e A354703 12 | 4, 8, 5, 8, 5, 8, 12, 8, 12, 8, 12, 16; | %e A354703 13 | 4, 8, 5, 7, 4, 6, 10, 6, 9, 4, 8, 12, 7 %e A354703 . %e A354703 T(4,3) = 3, because the optimally positioned and rotated 4 X 3 rectangle %e A354703 covers A354702(4,3) = 9 grid points, whereas a translated, but unrotated 4 X 3 rectangle covers 4*3 = 12 grid points. 4*3 - 9 = 3. %e A354703 + . . . . + . . . . + . . . . + . . . . + . . . . + . . . . + %e A354703 . . . . . . . %e A354703 . . . . . . . %e A354703 . . . . O . . . %e A354703 . . . . ~ \. . . %e A354703 + . . . . + . . . . + . . . . o . . . . \ . . . . + . . . . + %e A354703 . . . . .\ . . %e A354703 . . . ~ . . o . . %e A354703 . . o . . \ . . %e A354703 . . ~ . . . \ . . %e A354703 + . . . . + o . . . 1 . . . . 2 . . . . 3 . .\. . + . . . . + %e A354703 . ~ . . . . \ . . %e A354703 . O . . . . o . . %e A354703 . \ . . . . \ . . %e A354703 . \ . . . . \. . %e A354703 + . .\. . 4 . . . . 5 . . . . 6 . . . . 7 . . . . \ . . . . + %e A354703 . o . . . . .\ . %e A354703 . \ . . . . . O . %e A354703 . \ . . . . ~ . . %e A354703 . \. . . . o . . %e A354703 + . . . . \ . . . . 8 . . . . 9 . . . . + . . . . + . . . . + %e A354703 . .o . . ~ . . . %e A354703 . . \ . . o . . . %e A354703 . . \ . ~ . . . . %e A354703 . . \ . o . . . . %e A354703 + . . . . + . .\. . ~ . . . . + . . . . + . . . . + . . . . + %e A354703 . . O . . . . . %e A354703 . . . . . . %e A354703 . O---------o---------o---------o---------O . %e A354703 . | . . . . | . %e A354703 + . . | . 1 . . . . 2 . . . . 3 . . . . 4 . . | . + %e A354703 . | . . . . | . %e A354703 . | . . . . | . %e A354703 . o . . . . o . %e A354703 . | . . . . | . %e A354703 + . . | . 5 . . . . 6 . . . . 7 . . . . 8 . . | . + %e A354703 . | . . . . | . %e A354703 . | . . . . | . %e A354703 . o . . . . o . %e A354703 . | . . . . | . %e A354703 + . . | . 9 . . . .10 . . . .11 . . . .12 . . | . + %e A354703 . | . . . . | . %e A354703 . | . . . . | . %e A354703 . O---------o---------o---------o---------O . %e A354703 . . . . . . %e A354703 + . . . . + . . . . + . . . . + . . . . + . . . . + %Y A354703 Cf. A354702, A354492 (diagonal). %Y A354703 Cf. A354704, A354705 (similar, but for maximizing the number of covered points). %K A354703 nonn,tabl %O A354703 1,3 %A A354703 _Hugo Pfoertner_, Jun 15 2022