A371972 a(n) is the number of distinct areas of triangles with integer sides whose largest side is n.

1, 2, 4, 6, 9, 12, 16, 20, 25, 30, 36, 42, 49, 56, 64, 72, 81, 90, 100, 110, 120, 131, 144, 156, 168, 182, 196, 210, 225, 239, 256, 270, 288, 306, 321, 342, 361, 380, 399, 420, 441, 460, 484, 505, 527, 552, 576, 599, 623, 649, 673, 702, 729, 752, 781, 808, 840, 870, 900

Offset: 1

Author

Hugo Pfoertner, Apr 16 2024

Keywords

• nonn

Crossrefs

Cf. A316841, A371973, A371345.

See the formula section for the relationships with A002620, A173196, A316843, A316853.

Programs

PARI

A2(a,b,c) = {my(s=(a+b+c)/2);s*(s-a)*(s-b)*(s-c)};
a371972(n) = {my (A=List()); for(s2=1,n, for(s3=1,s2, if(s2+s3>n, listput(A, A2(n,s2,s3))))); #Set(A)};

Formula

a(n) <= A002620(n+1), with equality for n <= 20.

a(n) = |{A316853(k) : A316843(k) = n}| = |{A316853(k) : A173196(n) < k <= A173196(n+1)}|. - Peter Munn, Jul 30 2025