A088920 Solutions k to the Diophantine equation k = 2n^2 = m^2+1.

2, 50, 1682, 57122, 1940450, 65918162, 2239277042, 76069501250, 2584123765442, 87784138523762, 2982076586042450, 101302819786919522, 3441313796169221282, 116903366249966604050, 3971273138702695316402

Offset: 1

Author

Eric W. Weisstein, Oct 23 2003

Keywords

• nonn

Links

• Eric Weisstein's World of Mathematics, NSW Number
• Index entries for linear recurrences with constant coefficients, signature (35, -35, 1).

Crossrefs

Corresponding solutions of n are A001653 and m are A002315.

A008843(n-1) + 1.

Programs

Mathematica

Table[Round[N[ -(Sinh[(2 n - 1) ArcTanh[Sqrt[2]]])^2, 100]], {n, 1, 20}] (* Artur Jasinski, Oct 30 2008 *)

Formula

G.f.: (2x^2 - 20x + 2)/((1-x)(1 - 34x + x^2)).

a(n) = -(sinh((2n - 1) arctanh(sqrt(2))))^2 = 1 -(cosh((2n - 1) arctanh(sqrt(2))))^2. - Artur Jasinski, Oct 30 2008