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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. 2
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 (list; graph; refs; listen; history; text; internal format)
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: A198459 A083581 A171089 * A213761 A160248 A317858

Adjacent sequences:  A180492 A180493 A180494 * A180496 A180497 A180498

KEYWORD

nonn

AUTHOR

Carmine Suriano, Sep 08 2010

STATUS

approved

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Last modified May 11 15:04 EDT 2021. Contains 343791 sequences. (Running on oeis4.)