A237250 Values of x in the solutions to x^2 - 4xy + y^2 + 11 = 0, where 0 < x < y.

2, 3, 5, 10, 18, 37, 67, 138, 250, 515, 933, 1922, 3482, 7173, 12995, 26770, 48498, 99907, 180997, 372858, 675490, 1391525, 2520963, 5193242, 9408362, 19381443, 35112485, 72332530, 131041578, 269948677, 489053827, 1007462178, 1825173730, 3759900035

Offset: 1

Author

Colin Barker, Feb 05 2014

Keywords

• nonn
• easy

Comments

The corresponding values of y are given by a(n+2).

Positive values of x (or y) satisfying x^2 - 14xy + y^2 + 176 = 0.

Examples

			10 is in the sequence because (x, y) = (10, 37) is a solution to x^2 - 4xy + y^2 + 11 = 0.
		

Links

• Colin Barker, Table of n, a(n) for n = 1..1000
• Index entries for linear recurrences with constant coefficients, signature (0,4,0,-1).

Crossrefs

Cf. A001075, A001835, A003500, A082841.

Programs

PARI

Vec(-x*(x-1)*(x+2)*(2*x+1)/(x^4-4*x^2+1) + O(x^100))

Formula

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

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