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 A330912 #18 Feb 16 2025 08:33:59
%S A330912 3,5,5,6,5,14,38,8,20,11,37,29,43,7,31,64,11,17,37,84,19,15,70,130,22,
%T A330912 87,101,133,122,38,241,25,149,25,111,123,225,39,220,54,120,327,254,57,
%U A330912 103,162,227,371,41,321,34,43,29,278,373,76,70,95,577,567,157,476,221
%N A330912 Sum of the smallest side lengths of all Heronian triangles with perimeter A051518(n).
%H A330912 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/HeronianTriangle.html">Heronian Triangle</a>
%H A330912 Wikipedia, <a href="https://en.wikipedia.org/wiki/Heronian_triangle">Heronian triangle</a>
%H A330912 Wikipedia, <a href="https://en.wikipedia.org/wiki/Integer_triangle">Integer Triangle</a>
%F A330912 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)))) * k, where chi(n) = 1 - ceiling(n) + floor(n) and c(n) = A051518(n). - _Wesley Ivan Hurt_, May 12 2020
%e A330912 a(1) = 3; there is one Heronian triangle with perimeter A051518(1) = 12, which is [3,4,5] and its smallest side length is 3.
%e A330912 a(6) = 14; there are two Heronian triangles with perimeter A051518(6) = 32, [4,13,15] and [10,10,12]. The sum is 4 + 10 = 14.
%Y A330912 Cf. A051516, A051518, A070138, A096468, A298079, A298614, A305717.
%Y A330912 Cf. A330915, A330916.
%K A330912 nonn
%O A330912 1,1
%A A330912 _Wesley Ivan Hurt_, May 02 2020