0,1

a(n+1)/a(n) converges to ((27+sqrt(725))/2) =26.96291201... Lim a(n)/a(n+1) as n approaches infinity = 0.03708798... =2/(27+sqrt(725)) =(27-sqrt(725))/2. Lim a(n+1)/a(n) as n approaches infinity = 26.96291201... = (27+sqrt(725))/2=2/(27-sqrt(725)). Lim a(n)/a(n+1) = 27 - Lim a(n+1)/a(n).

A Chebyshev T-sequence with diophantine property.

a(n) gives the general (nonnegative integer) solution of the Pell equation a^2 - 29*(5*b)^2 =+4 with companion sequence b(n)=A097781(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.

Zerinvary Lajos, Sage Notebooks

a(n) =27a(n-1) - a(n-2), starting with a(0) = 2 and a(1) = 27. a(n) = ((27+sqrt(725))/2)^n + ((27-sqrt(725))/2)^n, (a(n))^2 =a(2n)+2.

a(n) = S(n, 27) - S(n-2, 27) = 2*T(n, 27/2) with S(n, x) := U(n, x/2), S(-1, x) := 0, S(-2, x) := -1. S(n, 27)=A097781(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 := (27+5*sqrt(29))/2 and am := (27-5*sqrt(29))/2.

G.f.: (2-27*x)/(1-27*x+x^2).

a(4) =528527 = 27a(3) - a(2) = 27*19602 - 727= ((27+sqrt(725))/2)^4 + ((27-sqrt(725))/2)^4 = 528526.999998107 + 0.000001892 =528527.

(x;y) = (2;0), (27;1), (727;27), (19602;728), ... give the nonnegative integer solutions to x^2 - 29*(5*y)^2 =+4.

a[0] = 2; a[1] = 27; a[n_] := 27a[n - 1] - a[n - 2]; Table[ a[n], {n, 0, 15}] (from Robert G. Wilson v Jan 30 2004)

sage: [lucas_number2(n, 27, 1) for n in xrange(0, 16)] - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Jun 27 2008

Cf. A046213, A078046.

a(n)=sqrt(4 + 29*(5*A097781(n-1))^2), n>=1.

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

Cf. A090733 for 2*T(n, 25/2).

Sequence in context: A121971 A121137 A138458 this_sequence A078102 A067075 A015217

Adjacent sequences: A090245 A090246 A090247 this_sequence A090249 A090250 A090251

easy,nonn

Nikolay V. Kosinov (kosinov(AT)unitron.com.ua), Jan 24 2004

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

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