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a(n) is the number of distinct areas > 0 of triangles with integer sides and perimeter n.
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%I #11 Oct 14 2024 11:33:56

%S 1,0,1,1,2,1,3,2,4,3,5,4,7,5,8,7,10,8,12,10,14,12,16,13,19,14,21,19,

%T 23,20,27,23,30,27,32,29,35,32,39,34,44,39,48,43,52,47,55,51,60,53,63,

%U 59,69,58,74,67,78,73,84,75,90,81,92,88,101,91,108,93,112,106

%N a(n) is the number of distinct areas > 0 of triangles with integer sides and perimeter n.

%H Hugo Pfoertner, <a href="/A371973/b371973.txt">Table of n, a(n) for n = 3..10000</a>

%o (PARI) A2(a,b,c) = {my (s=(a+b+c)/2); s*(s-a)*(s-b)*(s-c)};

%o a371973(n) = {my (A=List()); forpart (v=n, listput(A, A2(v[1],v[2],v[3])), [1,(n-1)\2], [3,3]); #Set(A)};

%Y Cf. A005044, A007237, A024153, A070083, A316841, A317182, A371070.

%K nonn

%O 3,5

%A _Hugo Pfoertner_, Apr 16 2024