A198386 Third of a triple of squares in arithmetic progression.

49, 196, 289, 441, 529, 784, 961, 1156, 1225, 1681, 1764, 2116, 2209, 2401, 2401, 2601, 3136, 3844, 3969, 4624, 4761, 4900, 5041, 5329, 5929, 6241, 6724, 7056, 7225, 7921, 8281, 8464, 8649, 8836, 9409, 9604, 9604, 10404, 10609, 11025, 12544, 12769, 13225

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) = A198390(n)^2.

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

A198437(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, 3]] (* Jean-François Alcover, Oct 19 2021 *)

Prog

(Haskell)
a198386 n = a198386_list !! (n-1)
a198386_list = map (^ 2) a198390_list

Crossrefs

Sequence in context: A244184 A251214 A158638 * A351663 A016982 A157919

Adjacent sequences: A198383 A198384 A198385 * A198387 A198388 A198389

Keyword

nonn

Author

Reinhard Zumkeller, Oct 24 2011

Status

approved