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A198949 y-values in the solution to 11*x^2-10 = y^2. 5
1, 23, 43, 461, 859, 9197, 17137, 183479, 341881, 3660383, 6820483, 73024181, 136067779, 1456823237, 2714535097, 29063440559, 54154634161, 579811987943, 1080378148123, 11567176318301, 21553408328299, 230763714378077, 429987788417857, 4603707111243239 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

When are both n+1 and 11*n+1 perfect squares? This problem gives the equation 11*x^2-10 = y^2.

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 1..250

Index entries for linear recurrences with constant coefficients, signature (0, 20, 0, -1).

FORMULA

a(n+4) = 20*a(n+2)-a(n) with a(1)=1, a(2)=23, a(3)=43, a(4)=461.

G.f.: x*(1+x)*(1+22*x+x^2)/(1-20*x^2+x^4). - Bruno Berselli, Nov 04 2011

a(n) = ((-(-1)^n-t)*(10-3*t)^floor(n/2)+(-(-1)^n+t)*(10+3*t)^floor(n/2))/2 where t=sqrt(11). - Bruno Berselli, Nov 14 2011

MATHEMATICA

LinearRecurrence[{0, 20, 0, -1}, {1, 23, 43, 461}, 24]  (* Bruno Berselli, Nov 11 2011 *)

PROG

(Maxima) makelist(expand(((-(-1)^n-sqrt(11))*(10-3*sqrt(11))^floor(n/2)+(-(-1)^n+sqrt(11))*(10+3*sqrt(11))^floor(n/2))/2), n, 1, 24);  /* Bruno Berselli, Nov 14 2011 */

CROSSREFS

Cf. A198947.

Sequence in context: A180534 A138975 A168439 * A214891 A003859 A058545

Adjacent sequences:  A198946 A198947 A198948 * A198950 A198951 A198952

KEYWORD

nonn,easy

AUTHOR

Sture Sjöstedt, Oct 31 2011

EXTENSIONS

More terms from Bruno Berselli, Nov 04 2011

STATUS

approved

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Last modified December 11 23:44 EST 2019. Contains 329945 sequences. (Running on oeis4.)