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 A330916 #20 Apr 12 2025 06:31:44
%S A330916 5,6,8,10,13,27,61,17,35,20,59,41,96,25,80,139,30,26,57,157,37,37,140,
%T A330916 296,40,196,207,250,209,91,587,52,294,51,267,214,498,50,539,117,310,
%U A330916 697,530,147,206,342,503,856,73,744,75,68,85,550,793,256,172,155,1270,1202
%N A330916 Sum of the largest side lengths of all Heronian triangles with perimeter A051518(n).
%H A330916 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/HeronianTriangle.html">Heronian Triangle</a>
%H A330916 Wikipedia, <a href="https://en.wikipedia.org/wiki/Heronian_triangle">Heronian triangle</a>
%H A330916 Wikipedia, <a href="https://en.wikipedia.org/wiki/Integer_triangle">Integer Triangle</a>
%F A330916 a(n) = Sum_{k=1..floor(c(n)/3)} Sum_{i=k..floor((c(n)-k)/2)} sign(floor((i+k)/(c(n)-i-k+1))) * chi(sqrt((c(n)/2)*(c(n)/2-i)*(c(n)/2-k)*(c(n)/2-(c(n)-i-k)))) * (c(n)-i-k), where chi(n) = 1 - ceiling(n) + floor(n) and c(n) = A051518(n). - _Wesley Ivan Hurt_, May 12 2020
%e A330916 a(1) = 5; there is one Heronian triangle with perimeter A051518(1) = 12, which is [3,4,5] and its largest side length is 5.
%e A330916 a(6) = 27; there are two Heronian triangles with perimeter A051518(6) = 32, [4,13,15] and [10,10,12]. The sum is 15 + 12 = 27.
%Y A330916 Cf. A051516, A051518, A070138, A096468, A298079, A298614, A305717.
%Y A330916 Cf. A330912, A330915.
%K A330916 nonn
%O A330916 1,1
%A A330916 _Wesley Ivan Hurt_, May 02 2020