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

2,1

Comments

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

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

Links

Table of n, a(n) for n=2..56.

Example

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.

Sequence in context: A083581 A171089 A368257 * A213761 A160248 A356044

Adjacent sequences: A180492 A180493 A180494 * A180496 A180497 A180498

Keyword

nonn

Author

Carmine Suriano, Sep 08 2010

Status

approved