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%I #15 Feb 01 2021 21:21:07
%S 6,12,12,24,30,72,198,60,126,66,288,180,360,84,330,648,132,204,420,
%T 876,114,156,840,1764,264,1350,1632,2016,1830,624,3816,330,2604,456,
%U 2280,2352,4800,780,4422,1224,2940,7068,5430,912,2310,3744,5520,9144,984,8736,1020
%N Sum of the areas of all Heronian triangles with perimeter A051518(n).
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/HeronianTriangle.html">Heronian Triangle</a>
%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Heronian_triangle">Heronian triangle</a>
%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Integer_triangle">Integer Triangle</a>
%F 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)))) * sqrt((c(n)/2)*(c(n)/2-i)*(c(n)/2-k)*(c(n)/2-(c(n)-i-k)), where chi(n) = 1 - ceiling(n) + floor(n) and c(n) = A051518(n). - _Wesley Ivan Hurt_, May 12 2020
%e a(1) = 6; there is one Heronian triangle with perimeter A051518(1) = 12, which is [3,4,5] and its area is 3*4/2 = 6.
%e a(6) = 72; there are two Heronian triangles with perimeter A051518(6) = 32, [4,13,15] and [10,10,12]. The sum of their areas 24 + 48 = 72.
%Y Cf. A051516, A051518, A070138, A096468, A298079, A298614, A305717.
%Y Cf. A330912, A330915, A330916.
%K nonn
%O 1,1
%A _Wesley Ivan Hurt_, May 02 2020