A281064 Values of x such that x^2 = 5*y^2 + 11, where x and y are positive integers.

4, 16, 56, 284, 1004, 5096, 18016, 91444, 323284, 1640896, 5801096, 29444684, 104096444, 528363416, 1867934896, 9481096804, 33518731684, 170131379056, 601469235416, 3052883726204, 10792927505804, 54781775692616, 193671225869056, 983019078740884

Offset: 1

Author

Colin Barker, Jan 14 2017

Keywords

• nonn
• easy

Comments

The corresponding values of y are in A082651.

Examples

			56 is in the sequence because 56^2 = 3136 = 5*25^2+11.
		

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).

Crossrefs

Cf. A082651.

Programs

Mathematica

LinearRecurrence[{0,18,0,-1},{4,16,56,284},30] (* Harvey P. Dale, May 28 2020 *)

PARI

Vec(4*x*(1 - x)*(1 + 5*x + x^2) / ((1 + 4*x - x^2)*(1 - 4*x - x^2)) + O(x^30))

Formula

a(n) = ((-2-r)^n*(r-5) + (5+r)*(r-2)^n + (15+7*r)*(r+2)^n + (2-r)^n*(7*r-15)) / (4*r) where r=sqrt(5).

a(n) = 18*a(n-2) - a(n-4) for n>3.

G.f.: 4*x*(1 - x)*(1 + 5*x + x^2) / ((1 + 4*x - x^2)*(1 - 4*x - x^2)).