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 A374594 Areas of trapezoids with integer sides and height whose area equals their perimeter. 1
 16, 18, 20, 20, 24, 30, 30, 36, 48, 70, 90, 180, 180, 420, 528, 870, 1170, 2610 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS A trapezoid is a quadrilateral with at least one pair of parallel sides. Conjecture: in this sequence are only three terms which belong to trapezoids with exactly one pair of parallel sides: a(3) = 20, a(5) = 24, a(7) = 30. LINKS Table of n, a(n) for n=1..18. Felix Huber, Illustration of terms a(1) to a(10). Felix Huber, Sides and heights of the trapezoids belonging to the terms a(1) to a(18). Eric Weisstein's World of Mathematics,Trapezoid. Wikipedia, Trapezoid. EXAMPLE See attached illustration of the terms a(1) to a(10). MAPLE with(NumberTheory): A374594:=proc(k); local K, L, S, T, i, a, c, x, y, h, b, d; L := Divisors(k); 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:=sqrt(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); CROSSREFS Cf. A098030, A181945, A189415, A214602, A272459, A335187, A340858, A348143, A360790. Sequence in context: A085096 A043675 A043705 * A178980 A031315 A077914 Adjacent sequences: A374591 A374592 A374593 * A374595 A374596 A374598 KEYWORD nonn,more AUTHOR Felix Huber, Jul 13 2024 STATUS approved

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Last modified September 16 22:04 EDT 2024. Contains 375979 sequences. (Running on oeis4.)