

A198949


yvalues in the solution to 11*x^210 = 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
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OFFSET

1,2


COMMENTS

When are both n+1 and 11*n+1 perfect squares? This problem gives the equation 11*x^210 = 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)/(120*x^2+x^4).  Bruno Berselli, Nov 04 2011
a(n) = (((1)^nt)*(103*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)^nsqrt(11))*(103*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



