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 A279413 #10 Feb 28 2017 09:25:46 %S A279413 0,0,4,0,2,12,0,0,6,16,0,2,4,6,24,0,0,2,8,10,28,0,2,4,2,8,6,36,0,0,2, %T A279413 0,6,8,10,40,0,2,4,2,12,10,8,10,56,0,0,2,4,2,4,10,8,10,60,0,2,4,2,4,2, %U A279413 12,6,12,6,60,0,0,2,0,2,4,6,12,6,8,14,64,0,2 %N A279413 Triangle read by rows: T(n,k), n>=k>=1, is the number of isosceles triangles with integer coordinates that have a bounding box of size n X k. %H A279413 Lars Blomberg, <a href="/A279413/b279413.txt">Table of n, a(n) for n = 1..9870</a> (the first 140 rows) %H A279413 Lars Blomberg, <a href="/A279413/a279413.pdf">Algorithms for computing A279413, A279414, A186434 and A271908</a> %e A279413 Triangle begins: %e A279413 0 %e A279413 0, 4 %e A279413 0, 2, 12 %e A279413 0, 0, 6, 16 %e A279413 0, 2, 4, 6, 24 %e A279413 0, 0, 2, 8, 10, 28 %e A279413 0, 2, 4, 2, 8, 6, 36 %e A279413 0, 0, 2, 0, 6, 8, 10, 40 %e A279413 0, 2, 4, 2, 12, 10, 8, 10, 56 %e A279413 0, 0, 2, 4, 2, 4, 10, 8, 10, 60 %e A279413 0, 2, 4, 2, 4, 2, 12, 6, 12, 6, 60 %e A279413 0, 0, 2, 0, 2, 4, 6, 12, 6, 8, 14, 64 %e A279413 0, 2, 4, 2, 4, 6, 8, 10, 16, 14, 12, 14, 72 %e A279413 0, 0, 2, 0, 2, 4, 2, 8, 14, 4, 6, 12, 18, 76 %e A279413 0, 2, 4, 2, 4, 2, 8, 2, 8, 10, 16, 10, 12, 10, 84 %e A279413 0, 0, 2, 0, 6, 4, 2, 4, 6, 16, 6, 4, 10, 12, 14, 88 %e A279413 0, 2, 4, 2, 4, 2, 8, 2, 16, 6, 16, 10, 16, 6, 24, 10, 104 %e A279413 0, 0, 2, 0, 2, 0, 2, 4, 6, 4, 10, 12, 10, 12, 10, 12, 14, 100 %e A279413 0, 2, 4, 2, 4, 2, 12, 6, 4, 6, 12, 10, 20, 6, 12, 14, 16, 10, 124 %e A279413 0, 0, 2, 0, 2, 0, 2, 0, 2, 4, 6, 12, 10, 12, 10, 12, 18, 12, 10, 112 %e A279413 ----- %e A279413 Denote by 'o' the point adjacent to the two equal sides, and by 'x' the other two. %e A279413 n=4, k=3: %e A279413 ...x x... .o.. ..o. x... ...x %e A279413 o... ...o ...x x... ...x x... %e A279413 ...x x... x... ...x .o.. ..o. %e A279413 So T(4,3)=6. %e A279413 ----- %e A279413 n=4,k=4: %e A279413 o... ...o .x.. ..x. o... ...o ..x. .x.. %e A279413 ...x x... .... .... .... .... ...x x... %e A279413 .... .... ...x x... ...x x... .... .... %e A279413 .x.. ..x. o... ...o ..x. .x.. o... ...o %e A279413 - %e A279413 ...x x... x... ...x o..x x..o x... ...x %e A279413 .o.. ..o. .... .... .... .... .... .... %e A279413 .... .... .o.. ..o. .... .... .... .... %e A279413 x... ...x ...x x... x... ...x o..x x..o %e A279413 So T(4,4)=16. %Y A279413 Cf. A186434, A187452, A271910-A271913, A271915, A279414. %Y A279413 See A279415 for right isosceles triangles. %Y A279413 See A280639 for obtuse isosceles triangles. %Y A279413 See A279418 for acute isosceles triangles. %Y A279413 See A279433 for all right triangles. %Y A279413 See A280652 for all obtuse triangles. %Y A279413 See A280653 for all acute triangles. %Y A279413 See A279432 for all triangles. %K A279413 nonn,tabl %O A279413 1,3 %A A279413 _Lars Blomberg_, Feb 16 2017