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 A330915 #19 Apr 12 2025 06:31:40
%S A330915 4,5,5,8,12,23,45,15,29,13,48,30,77,24,69,117,25,25,46,119,20,26,110,
%T A330915 246,26,167,172,205,169,79,468,33,229,38,222,167,429,41,429,101,270,
%U A330915 560,416,100,153,276,390,717,50,615,61,61,60,404,634,214,130,130,1033,975,382
%N A330915 Sum of the "middle" side lengths (b such that a <= b <= c) of all Heronian triangles with perimeter A051518(n).
%H A330915 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/HeronianTriangle.html">Heronian Triangle</a>
%H A330915 Wikipedia, <a href="https://en.wikipedia.org/wiki/Heronian_triangle">Heronian triangle</a>
%H A330915 Wikipedia, <a href="https://en.wikipedia.org/wiki/Integer_triangle">Integer Triangle</a>
%F A330915 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)))) * i, where chi(n) = 1 - ceiling(n) + floor(n) and c(n) = A051518(n). - _Wesley Ivan Hurt_, May 12 2020
%e A330915 a(1) = 4; there is one Heronian triangle with perimeter A051518(1) = 12, which is [3,4,5] and its "middle" side length is 4.
%e A330915 a(6) = 23; there are two Heronian triangles with perimeter A051518(6) = 32, [4,13,15] and [10,10,12]. The sum is 13 + 10 = 23.
%Y A330915 Cf. A051516, A051518, A070138, A096468, A298079, A298614, A305717.
%Y A330915 Cf. A330912, A330916.
%K A330915 nonn
%O A330915 1,1
%A A330915 _Wesley Ivan Hurt_, May 02 2020