A198949 y-values in the solution to 11*x^2-10 = y^2.

1, 23, 43, 461, 859, 9197, 17137, 183479, 341881, 3660383, 6820483, 73024181, 136067779, 1456823237, 2714535097, 29063440559, 54154634161, 579811987943, 1080378148123, 11567176318301, 21553408328299, 230763714378077, 429987788417857, 4603707111243239

Offset: 1

Author

Sture Sjöstedt, Oct 31 2011

Keywords

• nonn
• easy

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).

Crossrefs

Cf. A198947.

Programs

Mathematica

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

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 */

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

Extensions

More terms from Bruno Berselli, Nov 04 2011