0,2

a(n+1)^2 -10*(6*A078987(n))^2 = 1, n>=0 (Pell equation +1, see A033313 and A033317).

Also gives solutions to the equation x^2-1=floor(x*r*floor(x/r)) where r=sqrt(10) - Benoit Cloitre (benoit7848c(AT)orange.fr), Feb 14 2004

Tanya Khovanova, Recursive Sequences

Index entries for sequences related to Chebyshev polynomials.

a(n)=38*a(n-1) - a(n-2), a(-1) := 19, a(0)=1.

G.f.: (1-19*x)/(1-38*x+x^2).

a(n) = T(n, 19) = (S(n, 38)-S(n-2, 38))/2 = S(n, 38)-19*S(n-1, 38) with T(n, x), resp. S(n, x), Chebyshev's polynomials of the first, resp. second, kind. See A053120 and A049310. S(n, 38) = A078987(n).

a(n)= (ap^n + am^n)/2 with ap := 19+6*sqrt(10) and am := 19-6*sqrt(10).

a(n)= sum(((-1)^k)*(n/(2*(n-k)))*binomial(n-k, k)*(2*19)^(n-2*k), k=0..floor(n/2)), n>=1.

a(n) = Cosh[2n*ArcSinh[3]] - Herbert Kociemba (kociemba(AT)t-online.de), Apr 24 2008

(Other) sage: [lucas_number2(n, 38, 1)/2 for n in xrange(0, 16)]# [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Nov 07 2009]

Sequence in context: A119555 A107118 A162012 this_sequence A041687 A041684 A157165

Adjacent sequences: A078983 A078984 A078985 this_sequence A078987 A078988 A078989

nonn,easy,new

Wolfdieter Lang (wolfdieter.lang(AT)physik.uni-karlsruhe.de), Jan 10 2003