0,1

A Chebyshev T-sequence with diophantine property.

a(n) gives the general (nonnegative integer) solution of the Pell equation a^2 - 69*(3*b)^2 =+4 together with the companion sequence b(n)=A097780(n-1), n>=0.

O. Perron, "Die Lehre von den Kettenbruechen, Bd.I", Teubner, 1954, 1957 (Sec. 30, Satz 3.35, p. 109 and table p. 108).

Tanya Khovanova, Recursive Sequences

Index entries for recurrences a(n) = k*a(n - 1) +/- a(n - 2)

Index entries for sequences related to Chebyshev polynomials.

a(n) = S(n, 25) - S(n-2, 25) = 2*T(n, 25/2) with S(n, x) := U(n, x/2), S(-1, x) := 0, S(-2, x) := -1. S(n, 25)=A097780(n). U-, resp. T-, are Chebyshev's polynomials of the second, resp. first, kind. See A049310 and A053120.

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

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

a[0] = 2; a[1] = 25; a[n_] := 25a[n - 1] - a[n - 2]; Table[ a[n], {n, 0, 15}] (from Robert G. Wilson v Jan 30 2004)

sage: [lucas_number2(n, 25, 1) for n in xrange(0, 20)] - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Jun 26 2008

Cf. A046069, A082974.

a(n)=sqrt(4 + 69*(3*A097780(n-1))^2), n>=1.

Cf. A077428, A078355 (Pell +4 equations).

Cf. A097779 for 2*T(n, 23/2).

Adjacent sequences: A090730 A090731 A090732 this_sequence A090734 A090735 A090736

Sequence in context: A085830 A074209 A121252 this_sequence A119829 A059363 A014050

easy,nonn

Nikolay V. Kosinov (kosinov(AT)unitron.com.ua), Jan 18 2004

More terms from Robert G. Wilson v (rgwv(AT)rgwv.com), Jan 30 2004

Extension, Chebyshev and Pell comments from W. Lang (wolfdieter.lang(AT)physik.uni-karlsruhe.de), Aug 31 2004