0,2

a(n) gives the length of the word obtained after n steps with the substitution rule 0->1^9, 1->(1^9)0, starting from 0. The number of 1's and 0's of this word is 9*a(n-1) and 9*a(n-2), resp.

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

W. Lang, On polynomials related to powers of the generating function of Catalan's numbers, Fib. Quart. 38,5 (2000) 408-419; Eqs.(39) and (45),rhs, m=9.

Index entries for sequences related to linear recurrences with constant coefficients

Tanya Khovanova, Recursive Sequences

Index entries for sequences related to Chebyshev polynomials.

a(n) = 9*(a(n-1)+a(n-2)), a(-1)=0, a(0)=1.

a(n)= S(n, i*3)*(-i*3)^n with S(n, x) := U(n, x/2), Chebyshev's polynomials of the 2nd kind, A049310.

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

a(n)=Sum_{k, 0<=k<=n}8^k*A063967(n,k) . - Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Nov 03 2006

a(n)=(1/39)*[(9/2)+(3/2)*sqrt(13)]^(n+1)*sqrt(13)-(1/39)*sqrt(13)*[(9/2)-(3/2)*sqrt(13)]^(n+1), with n>=0 [From Paolo P. Lava (ppl(AT)spl.at), Nov 20 2008]

(Other) sage: [lucas_number1(n, 9, -9) for n in xrange(1, 20)]# [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Apr 26 2009]

Sequence in context: A054616 A052386 A158609 this_sequence A156577 A052268 A155199

Adjacent sequences: A057089 A057090 A057091 this_sequence A057093 A057094 A057095

nonn,easy

Wolfdieter Lang (wolfdieter.lang(AT)physik.uni-karlsruhe.de) Aug 11 2000