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 A351699 #25 Jul 14 2022 16:41:20
%S A351699 1,1,1,1,2,1,1,1,5,10,1,5,28,7,21,2,19,8,104,330,2,1,4,70,15,110,574,
%T A351699 1,3,30,272,205,4,71,563,1991,4,68,50,1001,113,1130,4,76,383,9,8,362,
%U A351699 35,1150,23,363,3975,7,38,8,18,1082,415,2,638,7503,23,515,5802,2,2,150,62,4238,120,1,55,1776,17277,26,481,2388
%N A351699 T(n,k) is the number of non-congruent maximal subsets of a grid of n X k lattice points (k <= n), such that no two points are at the same distance, and the points do not fit into a smaller grid. The size of the subsets is given by A351700. T(n,k) and A351700 are triangles read by rows.
%C A351699 Configurations of points differing by any combination of rotation and reflection are counted only once.
%H A351699 Hugo Pfoertner, <a href="/A351699/b351699.txt">Table of n, a(n) for n = 1..91</a>, rows 1..13 of triangle, flattened
%e A351699 The triangle begins:
%e A351699 #
%e A351699 # 1: 1 Counting grids n X k.
%e A351699 ( 1 ) Two lines per side length n:
%e A351699 # 2: 2 2 1. for other side k = 1, 2, ...
%e A351699 ( 1 1 ) maximal number of points
%e A351699 # 3: 2 3 3 2. number of configurations
%e A351699 ( 1 2 1 )
%e A351699 # 4: 3 4 4 4 Example: 28 figures with
%e A351699 ( 1 1 5 10 ) 4 points on 5 X 3
%e A351699 # 5: 3 4 4 5 5
%e A351699 ( 1 5 28 7 21 )
%e A351699 # 6: 3 4 5 5 5 6
%e A351699 ( 2 19 8 104 330 2 )
%e A351699 # 7: 4 5 5 6 6 6 7
%e A351699 ( 1 4 70 15 110 574 1 )
%e A351699 # 8: 4 5 5 6 7 7 7 7
%e A351699 ( 3 30 272 205 4 71 563 1991 )
%e A351699 # 9: 4 5 6 6 7 7 8 8 8
%e A351699 ( 4 68 50 1001 113 1130 4 76 383 )
%e A351699 #10: 4 6 6 7 7 8 8 8 9 9
%e A351699 ( 9 8 362 35 1150 23 363 3975 7 38 )
%e A351699 #11: 4 6 6 7 8 8 8 9 9 9 10
%e A351699 ( 8 18 1082 415 2 638 7503 23 515 5802 2 )
%e A351699 #
%e A351699 # Grid n X k configurations with
%e A351699 # distinct distances
%e A351699 .
%e A351699 .
%e A351699 All T(6,3) = 8 configurations
%e A351699 0 1 2 3 4 5 0 1 2 3 4 5
%e A351699 ------------------- -------------------
%e A351699 2 | . X X . X . 2 | . . . . X .
%e A351699 1 | . . . . . X 1 | . . . . . X
%e A351699 0 | X . . . . . 0 | X . X . . X
%e A351699 y /------------------- y /-------------------
%e A351699 x 0 1 2 3 4 5 x 0 1 2 3 4 5
%e A351699 {1,2,4,5,8,9,10,17,20,26} dist^2 {1,2,4,5,8,9,10,20,25,26}
%e A351699 0 1 2 3 4 5 0 1 2 3 4 5
%e A351699 ------------------- -------------------
%e A351699 2 | . . X . X . 2 | . X . X . .
%e A351699 1 | . . . . . X 1 | X . . . . .
%e A351699 0 | X X . . . . 0 | X . . . . X
%e A351699 y /------------------- y /-------------------
%e A351699 x 0 1 2 3 4 5 x 0 1 2 3 4 5
%e A351699 {1,2,4,5,8,10,13,17,20,26} dist^2 {1,2,4,5,8,10,13,20,25,26}
%e A351699 0 1 2 3 4 5 0 1 2 3 4 5
%e A351699 ------------------- -------------------
%e A351699 2 | . . . . X . 2 | . . X . X .
%e A351699 1 | X . . . . X 1 | X . . . . X
%e A351699 0 | X . X . . . 0 | X . . . . .
%e A351699 y /------------------- y /-------------------
%e A351699 x 0 1 2 3 4 5 x 0 1 2 3 4 5
%e A351699 {1,2,4,5,8,10,17,20,25,26} dist^2 {1,2,4,5,8,10,17,20,25,26}
%e A351699 0 1 2 3 4 5 0 1 2 3 4 5
%e A351699 ------------------- -------------------
%e A351699 2 | . . X . . X 2 | X . . . . X
%e A351699 1 | . . . . . . 1 | . . . . . .
%e A351699 0 | X X . . . X 0 | X . . X X .
%e A351699 y /------------------- y /-------------------
%e A351699 x 0 1 2 3 4 5 x 0 1 2 3 4 5
%e A351699 {1,4,5,8,9,13,16,20,25,29} dist^2 {1,4,5,8,9,13,16,20,25,29}
%e A351699 .
%Y A351699 Cf. A193838, A193839, A271490, A325677, A335232, A351700, A351701.
%K A351699 nonn,tabl,hard
%O A351699 1,5
%A A351699 _Rainer Rosenthal_ and _Hugo Pfoertner_, Apr 09 2022
%E A351699 Completed row 8 and new rows 9-12 from _Hugo Pfoertner_, Jul 12 2022