A374594 Areas of trapezoids with integer sides and height whose area equals their perimeter.
16, 18, 18, 20, 20, 24, 30, 30, 36, 48, 70, 90, 180, 180, 420, 528, 870, 1170, 2610
Offset: 1
Examples
See attached illustration of the terms a(1) to a(11).
Links
- Felix Huber, Illustration of terms a(1) to a(11)
- Felix Huber, Sides and heights of the trapezoids belonging to the terms a(1) to a(19)
- Eric Weisstein's World of Mathematics,Trapezoid.
- Wikipedia, Trapezoid.
Programs
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Maple
with(NumberTheory): A374594:=proc(k); local K,L,S,T,i,a,c,x,y,h,b,d; L:=map(x->x/2, Divisors(2*k) minus {1, 2}); S:=[]; T:=[]; K:=[]; for i to numelems(L) do for c to L[i] do a:=2*L[i]-c; h:=k/L[i]; x:=0; while x^2<(k-a-c)^2-h^2 do if issqr(x^2+h^2) then d:=isqrt(x^2+h^2); b:=k-a-c-d; y:=a-c-x; if h^2+y^2=b^2 then S:=[a,b,c,d]; S:=sort(S); if member(S,T)=false then T:=[op(T),S]; K:=[op(K),k]; fi; fi; fi; x:=x+1; od; od; od; if numelems(K)>0 then return op(K) fi; end proc; seq(A374594(k),k=1..3000);
Extensions
Corrected by Felix Huber, Dec 04 2024
Comments