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 A353533 #11 May 08 2022 08:23:34 %S A353533 1,2,1,2,2,3,3,3,4,6,3,5,5,8,9,4,4,6,12,12,12,4,4,12,8,11,15,14,5,5,8, %T A353533 10,15,15,20,18,5,5,8,27,15,33,32,26,25,6,6,10,11,17,17,23,22,29,29,6, %U A353533 6,10,12,48,18,24,29,30,42,34,7,7,16,14,21,21,41,69,34 %N A353533 T(n,m) with 4 <= m < n is the number of quadrilaterals in A353532 with perpendicular diagonals, where T(n,m) is a triangle read by rows. %e A353533 The quadrilaterals counted in A353532 with m = 3 or m = n cannot have perpendicular diagonals, and are therefore omitted in the triangle of this sequence. %e A353533 . %e A353533 \ m 3 4 5 6 7 8 9 10 11 %e A353533 n \----------------------------------- %e A353533 3 | 0, | | | | | | | | %e A353533 4 | 0, 0, | | | | | | | %e A353533 5 | 0, 1, 0, | | | | | | %e A353533 6 | 0, 2, 1, 0, | | | | | %e A353533 7 | 0, 2, 2, 3, 0, | | | | %e A353533 8 | 0, 3, 3, 4, 6, 0, | | | %e A353533 9 | 0, 3, 5, 5, 8, 9, 0, | | %e A353533 10 | 0, 4, 4, 6, 12, 12, 12, 0, | %e A353533 11 | 0, 4, 4, 12, 8, 11, 15, 14, 0 %e A353533 . %e A353533 T(5,4) = a(1) = 1: %e A353533 . %e A353533 4 | . C . . . Squared distances denoted %e A353533 3 | . . . . . as in examples A353532: %e A353533 2 | D . . . B %e A353533 1 | . A . . . AB-BC-CD-DA (around) %e A353533 y /---------- AC X DB (across) %e A353533 x 1 2 3 4 5 %e A353533 . %e A353533 10-13-5-2 %e A353533 9 X 16 %e A353533 . %e A353533 T(6,4) = a(2) = 2: %e A353533 . %e A353533 4 | . X . . . . 4 | . . X . . . %e A353533 3 | . . . . . . 3 | . . . . . . %e A353533 2 | X . . . . X 2 | X . . . . X %e A353533 1 | . X . . . . 1 | . . X . . . %e A353533 y /------------ y /------------ %e A353533 x 1 2 3 4 5 6 x 1 2 3 4 5 6 %e A353533 . %e A353533 17-20-5-2 10-13-8-5 %e A353533 9 X 25 9 X 25 %e A353533 . %e A353533 T(6,5) = a(3) = 1: %e A353533 . %e A353533 5 | . . X . . . %e A353533 4 | . . . . . . %e A353533 3 | . . . . . . 10-18-13-5 %e A353533 2 | X . . . . X 16 X 25 %e A353533 1 | . . X . . . %e A353533 y /------------ %e A353533 x 1 2 3 4 5 6 %e A353533 . %e A353533 T(9,5) = a(12) = 5; %e A353533 3 quadrilaterals with diagonals parallel to the grid axes: %e A353533 . %e A353533 5 | . X . . . . . . . 5 | . . X . . . . . . 5 | . . . X . . . . . %e A353533 4 | . . . . . . . . . 4 | . . . . . . . . . 4 | . . . . . . . . . %e A353533 3 | . . . . . . . . . 3 | . . . . . . . . . 3 | . . . . . . . . . %e A353533 2 | X . . . . . . . X 2 | X . . . . . . . X 2 | X . . . . . . . X %e A353533 1 | . X . . . . . . . 1 | . . X . . . . . . 1 | . . . X . . . . . %e A353533 y /------------------ y /------------------ y /------------------ %e A353533 x 1 2 3 4 5 6 7 8 9 x 1 2 3 4 5 6 7 8 9 x 1 2 3 4 5 6 7 8 9 %e A353533 . %e A353533 50-58-10-2 37-45-13-5 26-34-18-10 %e A353533 16 X 64 16 X 64 16 X 64 %e A353533 . %e A353533 The 2 quadrilaterals with diagonals not aligned with the grid axes are the smallest example of this type: %e A353533 . %e A353533 . %e A353533 5 | . X . . . . . . . 5 | . . X . . . . . . %e A353533 4 | . . . . . . . . X 4 | . . . . . . . . X %e A353533 3 | . . . . . . . . . 3 | . . . . . . . . . %e A353533 2 | X . . . . . . . . 2 | X . . . . . . . . %e A353533 1 | . . X . . . . . . 1 | . . . X . . . . . %e A353533 y /------------------ y /------------------ %e A353533 x 1 2 3 4 5 6 7 8 9 x 1 2 3 4 5 6 7 8 9 %e A353533 . %e A353533 45-50-10-5 34-37-13-10 %e A353533 17 X 68 17 X 68 %e A353533 . %Y A353533 Cf. A353447, A353532. %K A353533 nonn,tabl %O A353533 5,2 %A A353533 _Hugo Pfoertner_ and _Rainer Rosenthal_, May 04 2022