0,2

All positive integer solutions of Pell equation b(n)^2 - 621*a(n)^2 = +4 together with b(n)=A090733(n+1), n>=0. Note that D=621=69*3^2 is not square-free.

Tanya Khovanova, Recursive Sequences

Index entries for sequences related to Chebyshev polynomials.

Zerinvary Lajos, Sage Notebooks

a(n)= S(n, 25)=U(n, 25/2)= S(2*n+1, sqrt(25))/sqrt(25) with S(n, x)=U(n, x/2) Chebyshev's polynomials of the 2nd kind, A049310. S(-1, x)= 0 = U(-1, x).

a(n)=25*a(n-1)-a(n-2), n >= 1; a(0)=1, a(1)=25; a(-1)=0.

a(n)=(ap^(n+1) - am^(n+1))/(ap-am) with ap := (25+3*sqrt(69))/2 and am := (25-3*sqrt(69))/2.

G.f.: 1/(1-25*x+x^2).

(x,y) = (2,0), (25;1), (623;25), (15550;624), ... give the nonnegative integer solutions to x^2 - 69*(3*y)^2 =+4.

sage: [lucas_number1(n, 25, 1) for n in xrange(1, 20)] - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Jun 25 2008

Sequence in context: A014909 A104643 A061614 this_sequence A068180 A009969 A042202

Adjacent sequences: A097777 A097778 A097779 this_sequence A097781 A097782 A097783

nonn,easy

Wolfdieter Lang (wolfdieter.lang_AT_physik_DOT_uni-karlsruhe_DOT_de), Aug 31 2004