A180495 Coefficient a(n) of three-term recurrence relation for solutions of the equation in integers x^2-n*floor(x/sqrt(n))^2=1 such that x(i+2)=a(n)*x(i+1)-x(i). n is a nonsquare number.

6, 4, 18, 10, 16, 6, 38, 20, 14, 1298, 30, 8, 66, 34, 340, 18, 110, 394, 48, 10, 102, 52, 254, 19602, 22, 3040, 34, 46, 70, 12, 146, 74, 50, 38, 4098, 26, 6964, 398, 322, 48670, 96, 14, 198, 100, 1298, 132498, 970, 178, 30, 302, 39206, 1060, 62, 3532638098, 126

Offset: 2

Author

Carmine Suriano, Sep 08 2010

Keywords

• nonn

Comments

a(n) is twice the corresponding term of sequence A033313.

Nonsquare values belong to sequence A000037. The equation is of a Pell type.

Examples

			For n=3 a(3)=4 since equation x^2-3*floor(x/sqrt(3))^2=1 has the following solutions: x=1, 2, 7, 26, 97, ... for which x(i+2)=4x(i+1)-x(i).
		

Crossrefs

Cf. A000037, A033313.