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 A333919 #14 Feb 16 2025 08:33:59
%S A333919 12,24,30,36,40,42,48,56,60,70,72,78,80,84,90,96,104,108,110,112,114,
%T A333919 120,126,132,136,140,144,150,154,156,160,162,168,176,180,182,186,192,
%U A333919 198,200,204,208,210,216,220,222,224,228,230,232,234,238,240,250,252
%N A333919 Perimeters of integer-sided triangles with side lengths a <= b <= c whose altitude from side b is an integer.
%H A333919 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/Altitude.html">Altitude</a>
%H A333919 Wikipedia, <a href="https://en.wikipedia.org/wiki/Altitude_(triangle)">Altitude (triangle)</a>
%H A333919 Wikipedia, <a href="https://en.wikipedia.org/wiki/Integer_triangle">Integer Triangle</a>
%e A333919 12 is in the sequence since it is the perimeter of the triangle [3,4,5], whose altitude from 4 (its "middle" side) is 3 (an integer).
%e A333919 24 is in the sequence since it is the perimeter of the triangle [6,8,10], whose altitude from 8 (its "middle" side) is 6 (an integer).
%e A333919 60 is in the sequence since it is the perimeter of the triangles [10,24,26] and [15,20,25], whose altitudes (from their "middle" sides) are 10 and 15 respectively (both integers).
%t A333919 Flatten[Table[If[Sum[Sum[(1 - Ceiling[2*Sqrt[(n/2) (n/2 - i) (n/2 - k) (n/2 - (n - i - k))]/i] + Floor[2*Sqrt[(n/2) (n/2 - i) (n/2 - k) (n/2 - (n - i - k))]/i]) Sign[Floor[(i + k)/(n - i - k + 1)]], {i, k, Floor[(n - k)/2]}], {k, Floor[n/3]}] > 0, n, {}], {n, 100}]]
%Y A333919 Cf. A005044, A333917, A333918.
%K A333919 nonn
%O A333919 1,1
%A A333919 _Wesley Ivan Hurt_, Apr 09 2020