0,3

Define the sequence L(a_0,a_1) by a_{n+2} is the greatest integer such that a_{n+2}/a_{n+1}<a_{n+1}/a_n for n >= 0. This is L(1,9).

D. W. Boyd, Linear recurrence relations for some generalized Pisot sequences, Advances in Number Theory ( Kingston ON, 1991) 333-340, Oxford Sci. Publ., Oxford Univ. Press, New York, 1993;.

E. I. Emerson, Recurrent Sequences in the Equation DQ^2=R^2+N, Fib. Quart., 7 (1969).

A. F. Horadam, Special properties of the sequence W_n(a,b; p,q), Fib. Quart., 5.5 (1967), 424-434. Case a=0,b=1; p=9, q=-1.

W. Lang, On polynomials related to powers of the generating function of Catalan's numbers, Fib. Quart. 38,5 (2000) 408-419; Eq.(44), lhs, m=11.

Index entries for sequences related to linear recurrences with constant coefficients

Tanya Khovanova, Recursive Sequences

Index entries for sequences related to Chebyshev polynomials.

G.f.: 1/(1-9*x+x^2).

a(n) = S(2*n-1, sqrt(11))/sqrt(11) = S(n-1, 9); S(n, x) := U(n, x/2), Chebyshev polynomials of 2nd kind, A049310. S(-1, x) := 0.

a(n)={[(9+sqrt(77))/2]^n - [(9-sqrt(77))/2]^n}/sqrt(77). G.f.(x)=x/(1-9*x+x^2). - Barry E. Williams, Aug 21 2000

sage: [lucas_number1(n, 9, 1) for n in range(22)] - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Jun 25 2008

Cf. A000027, A001906, A001353, A004254, A001109, A004187, A001090.

Cf. A056918(n)=sqrt{77*(a(n))^2 +4}, that is, a(n)=sqrt((A056918(n)^2 - 4)/77).

Sequence in context: A083411 A171314 A081108 this_sequence A127265 A055070 A143848

Adjacent sequences: A018910 A018911 A018912 this_sequence A018914 A018915 A018916

easy,nonn

R. K. Guy (rkg(AT)cpsc.ucalgary.ca)

More terms from James A. Sellers (sellersj(AT)math.psu.edu), Sep 07 2000