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.
f:= proc(n) local a,b,q,bmin,bmax,t;
t:= 0;
for a from 1 to n/3 do
if n::even then bmin:= max(a+1,n/2-a+1) else bmin:= max(a+1,(n+1)/2-a) fi;
q:= (n^2-2*n*a)/(2*(n-a));
if q::integer then bmax:= min((n-a)/2, q-1) else bmax:= min((n-a)/2, floor(q)) fi;
t:= t + nops(select(b -> igcd(a,b,n-a-b) = 1, [$bmin .. bmax]))
od;
t
end proc:
map(f, [$1..100]); # Robert Israel, Jul 26 2024
There are five quadrilaterals with perimeter 8, with sides (1,1,3,3), (1,2,2,3), (1,2,3,2), (1,3,1,3) and (2,2,2,2). (2,2,2,2) is omitted since it has GCD=2, so a(8)=4.
For perimeter 24, only the triangle with a=6, b=8, c=10 has an integer inradius (2), therefore a(24)=1. The next examples are a(32)=1 with a=10, b=10, c=12 and a(36)=1 with a=9, b=12, c=15.