A082651 Positive integer values of n such that 5n^2+11 is a square.

1, 7, 25, 127, 449, 2279, 8057, 40895, 144577, 733831, 2594329, 13168063, 46553345, 236291303, 835365881, 4240075391, 14990032513, 76085065735, 268985219353, 1365291107839, 4826743915841, 24499154875367, 86612405265785, 439619496648767, 1554196550868289

Offset

1,2

Comments

The corresponding sequence for which 5n^2+4 is a square is A001906 (a bisection of the Fibonacci sequence).

Links

Colin Barker, Table of n, a(n) for n = 1..1000

Index entries for linear recurrences with constant coefficients, signature (0,18,0,-1).

Formula

a(n) = 18*a(n-2) - a(n-4).

G.f.: x*(1+7*x+7*x^2+x^3)/(1-18*x^2+x^4). - Colin Barker, Jun 14 2012

Example

25 is a term of the sequence since 5*25^2 + 11 = 56^2.

Mathematica

LinearRecurrence[{0, 18, 0, -1}, {1, 7, 25, 127}, 50] (* Paolo Xausa, Mar 18 2024 *)

Prog

(PARI) Vec(x*(1+7*x+7*x^2+x^3)/(1-18*x^2+x^4) + O(x^100)) \\ Colin Barker, Nov 06 2014

Crossrefs

Cf. A001906, A080806.

Sequence in context: A138292 A138738 A057573 * A241714 A151491 A208425

Adjacent sequences: A082648 A082649 A082650 * A082652 A082653 A082654

Keyword

nonn,easy

Author

John W. Layman, May 16 2003

Extensions

More terms from Colin Barker, Nov 06 2014

Status

approved