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 A353532 #28 Jun 09 2022 11:40:50 %S A353532 0,0,0,0,3,1,1,7,12,11,1,11,26,52,40,4,23,50,94,147,105,4,30,69,127, %T A353532 198,301,190,10,49,103,192,302,444,583,379,10,58,127,244,387,576,754, %U A353532 1039,616,18,84,180,329,509,756,989,1334,1680,987,18,94,209,389,611,910,1203,1618,2052,2581,1426 %N A353532 T(n,m) is the number of non-congruent quadrilaterals with integer vertex coordinates (x1,1), (n,y2), (x3,m), (1,y4), 1 < x1, x3 < n, 1 < y2, y4 < m, m <= n, such that the 6 distances between the 4 vertices are distinct. %C A353532 T(n,m) is a triangle, read by rows. %H A353532 Rainer Rosenthal, <a href="/A353532/b353532.txt">Rows n = 3..100, flattened</a> %H A353532 Hugo Pfoertner, <a href="/A353532/a353532.gp.txt">PARI program</a> %e A353532 The triangle begins %e A353532 \ m 3 4 5 6 7 8 9 10 %e A353532 n \------------------------------------- %e A353532 3 | 0, | | | | | | | %e A353532 4 | 0, 0, | | | | | | %e A353532 5 | 0, 3, 1, | | | | | %e A353532 6 | 1, 7, 12, 11, | | | | %e A353532 7 | 1, 11, 26, 52, 40, | | | %e A353532 8 | 4, 23, 50, 94, 147, 105, | | %e A353532 9 | 4, 30, 69, 127, 198, 301, 190, | %e A353532 10 | 10, 49, 103, 192, 302, 444, 583, 379 %e A353532 . %e A353532 . %e A353532 4 | . C . . . There are six squared distances. %e A353532 3 | . . . . . They are arranged as follows: %e A353532 2 | D . . . B AB-BC-CD-DA (counterclockwise) %e A353532 1 | . A . . . AC X DB (across) %e A353532 y /---------- Here: AB = 3^2 + 1^2 = 10, %e A353532 x 1 2 3 4 5 BC = 13, CD = 5, DA = 2, %e A353532 . AC = 9, DB = 16 %e A353532 10-13-5-2 <==== yielding this %e A353532 9 X 16 <==== description %e A353532 . %e A353532 . %e A353532 T(5,4) = a(5) = 3: %e A353532 . %e A353532 4 | . X . . . 4 | . X . . . 4 | . . X . . %e A353532 3 | . . . . . 3 | . . . . X 3 | . . . . X %e A353532 2 | X . . . X 2 | X . . . . 2 | X . . . . %e A353532 1 | . X . . . 1 | . X . . . 1 | . X . . . %e A353532 y /---------- y /---------- y /---------- %e A353532 x 1 2 3 4 5 x 1 2 3 4 5 x 1 2 3 4 5 %e A353532 . %e A353532 10-13-5-2 13-10-5-2 13-5-8-2 %e A353532 9 X 16 9 X 17 10 X 17 %e A353532 . %e A353532 T(5,5) = a(6) = A353447(5) = 1: %e A353532 . %e A353532 5 | . . . X . %e A353532 4 | . . . . . %e A353532 3 | . . . . X 13-5-18-2 %e A353532 2 | X . . . . 20 X 17 %e A353532 1 | . X . . . %e A353532 y /---------- %e A353532 x 1 2 3 4 5 %e A353532 . %e A353532 T(6,3) = a(7) = 1: %e A353532 . %e A353532 3 | . . . X . . %e A353532 2 | X . . . . X 17-5-10-2 %e A353532 1 | . X . . . . 8 X 25 %e A353532 y /------------ %e A353532 x 1 2 3 4 5 6 %e A353532 . %e A353532 T(6,4) = a(8) = 7: %e A353532 . %e A353532 4 | . X . . . . 4 | . X . . . . 4 | . . X . . . 4 | . . . X . . %e A353532 3 | . . . . . . 3 | . . . . . X 3 | . . . . . . 3 | X . . . . . %e A353532 2 | X . . . . X 2 | X . . . . . 2 | X . . . . X 2 | . . . . . X %e A353532 1 | . X . . . . 1 | . X . . . . 1 | . X . . . . 1 | . X . . . . %e A353532 y /------------ y /------------ y /------------ y /------------ %e A353532 x 1 2 3 4 5 6 x 1 2 3 4 5 6 x 1 2 3 4 5 6 x 1 2 3 4 5 6 %e A353532 . %e A353532 17-20-5-2 20-17-5-2 17-13-8-2 17-8-10-5 %e A353532 9 X 25 9 X 26 10 X 25 13 X 26 %e A353532 . %e A353532 4 | . . . . X . 4 | . . X . . . 4 | . . X . . . %e A353532 3 | . . . . . . 3 | . . . . . . 3 | . . . . . X %e A353532 2 | X . . . . X 2 | X . . . . X 2 | X . . . . . %e A353532 1 | . X . . . . 1 | . . X . . . 1 | . . X . . . %e A353532 y /------------ y /------------ y /------------ %e A353532 x 1 2 3 4 5 6 x 1 2 3 4 5 6 x 1 2 3 4 5 6 %e A353532 . %e A353532 17-5-20-2 10-13-8-5 13-10-8-5 %e A353532 18 X 25 9 X 25 9 X 26 %e A353532 . %o A353532 (PARI) see Pfoertner link. %Y A353532 Cf. A353447 (diagonal), A353449, A353450, A353451, A353533, A354700. %Y A353532 The general case without excluding the corners of the grid rectangle is covered in A354700 and A354701. %K A353532 nonn,tabl %O A353532 3,5 %A A353532 _Hugo Pfoertner_ and _Rainer Rosenthal_, May 02 2022