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

1,1

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

Formula

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

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

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

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 *)

Prog

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

Crossrefs

Sequence in context: A237202 A353152 A335717 * A134422 A016850 A309779

Adjacent sequences: A198382 A198383 A198384 * A198386 A198387 A198388

Keyword

nonn

Author

Reinhard Zumkeller, Oct 24 2011

Status

approved