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

1,1

Comments

The corresponding values of y are in A082651.

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) = ((-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)).

Example

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

Mathematica

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

Prog

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

Crossrefs

Cf. A082651.

Sequence in context: A201619 A197532 A220106 * A122032 A197674 A297220

Adjacent sequences: A281061 A281062 A281063 * A281065 A281066 A281067

Keyword

nonn,easy

Author

Colin Barker, Jan 14 2017

Status

approved