A198385 Second of a triple of squares in arithmetic progression.

25, 100, 169, 225, 289, 400, 625, 676, 625, 841, 900, 1156, 1369, 1225, 1681, 1521, 1600, 2500, 2025, 2704, 2601, 2500, 3721, 2809, 3025, 4225, 3364, 3600, 4225, 4225, 4225, 4624, 5625, 5476, 7225, 4900, 6724, 6084, 5329, 5625, 6400, 7225, 7225, 7225, 7921

Offset: 1

Author

Reinhard Zumkeller, Oct 24 2011

Keywords

• nonn

Links

• Ray Chandler, Table of n, a(n) for n = 1..10000
• Keith Conrad, Arithmetic progressions of three squares
• Reinhard Zumkeller, Table of initial values

Programs

Haskell

a198385 n = a198385_list !! (n-1)
a198385_list = map (^ 2) a198389_list

Mathematica

wmax = 1000;
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]];
Flatten[DeleteCases[triples /@ Range[wmax], {}], 2][[All, 2]] (* Jean-François Alcover, Oct 19 2021 *)

Formula

a(n) = A198389(n)^2.

a(n) - A198384(n) = A198386(n) - a(n) = A198387(n).

A198436(n) = a(A198409(n)).