A070146 -id:A070146 - cp's OEIS frontend

A070140 Number of acute integer triangles with perimeter n having integral area.

0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 1, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 2, 0, 0, 0, 0, 0, 1

Offset: 1

Reinhard Zumkeller, May 05 2002

nonn

a(n) = A051516(n) - A070141(n) - A024155(n).

Eric Weisstein's World of Mathematics, Heronian Triangle.
Eric Weisstein's World of Mathematics, Acute Triangle.
R. Zumkeller, Integer-sided triangles

Cf. A051516, A070093, A070146.

A070147 Numbers k such that [A070080(k), A070081(k), A070082(k)] is an obtuse integer triangle with integer area.

Original entry on oeis.org

52, 252, 368, 372, 561, 659, 839, 957, 1156, 1186, 1204, 1582, 1912, 1920, 1971, 2115, 2713, 2774, 2790, 3251, 3473, 3728, 3746, 4286, 4307, 4313, 4330, 5008, 5272, 5374, 6369, 6389, 6432, 6776, 6881, 7223, 7310, 7341

Offset: 1

Reinhard Zumkeller, May 05 2002

nonn

			a(1)=52: [A070080(52), A070081(52), A070082(52)] = [5,5,8]: A070085(52)=5^2+5^2-8^2=-14<0 and area^2 = s*(s-5)*(s-5)*(s-6) with s=A070083(52)/2=(5+5+8)/2=9, area^2=9*4*4*1=16*9 is an integer square, therefore A070086(52)=area=4*3=12.

Eric Weisstein's World of Mathematics, Heronian Triangle.
Eric Weisstein's World of Mathematics, Obtuse Triangle.
Reinhard Zumkeller, Integer-sided triangles

Cf. A070142, A070136, A070146, A070141.

cp's OEIS Frontend

A070140 Number of acute integer triangles with perimeter n having integral area.

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