A198386 - OEIS

%I #25 Oct 19 2021 12:10:03

%S 49,196,289,441,529,784,961,1156,1225,1681,1764,2116,2209,2401,2401,

%T 2601,3136,3844,3969,4624,4761,4900,5041,5329,5929,6241,6724,7056,

%U 7225,7921,8281,8464,8649,8836,9409,9604,9604,10404,10609,11025,12544,12769,13225

%N Third of a triple of squares in arithmetic progression.

%H Ray Chandler, <a href="/A198386/b198386.txt">Table of n, a(n) for n = 1..10000</a>

%H Keith Conrad, <a href="http://www.math.uconn.edu/~kconrad/blurbs/ugradnumthy/3squarearithprog.pdf">Arithmetic progressions of three squares</a>

%H Reinhard Zumkeller, <a href="/A198384/a198384_2.txt">Table of initial values</a>

%F a(n) = A198390(n)^2.

%F a(n) - A198385(n) = A198385(n) - A198384(n) = A198387(n).

%F A198437(n) = a(A198409(n)).

%t wmax = 1000;

%t triples[w_] := Reap[Module[{u, v}, For[u = 1, u < w, u++, If[IntegerQ[v = Sqrt[(u^2 + w^2)/2]], Sow[{u^2, v^2, w^2}]]]] ][[2]];

%t Flatten[DeleteCases[triples /@ Range[wmax], {}], 2][[All, 3]] (* _Jean-François Alcover_, Oct 19 2021 *)

%o (Haskell)

%o a198386 n = a198386_list !! (n-1)

%o a198386_list = map (^ 2) a198390_list

%K nonn

%O 1,1

%A _Reinhard Zumkeller_, Oct 24 2011