0,3

Define the sequence T(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 . A004178 (with initial 0 omitted) is T(1,7).

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=7, q=-1.

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;.

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=9.

Tanya Khovanova, Recursive Sequences

Index entries for sequences related to Chebyshev polynomials.

G.f.: x/(1-7*x+x^2). a(n)=F(4n)/3, where F=A000045 (the Fibonacci sequence).

a(n) = S(2*n-1, sqrt(9))/sqrt(9) = S(n-1, 7); S(n, x) := U(n, x/2), Chebyshev polynomials of 2nd kind, A049310.

a(n)=Sum(C(2n-1-i, i)5^(n-i-1), i=0, .., n-1). - Mario Catalani (mario.catalani(AT)unito.it), Jul 23 2004

a(n) = Fib(4n) / 3 - Jim Cullen (jtcullen(AT)lrbcg.com), Nov 11 2004

[A049685(n-1), a(n)] = [1,5; 1,6]^n * [1,0]. - Gary W. Adamson (qntmpkt(AT)yahoo.com), Mar 21 2008

(Mupad) numlib::fibonacci(4*n)/3 $ n = 0..25; - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), May 09 2008

Cf. A000027, A001906, A001353, A004254, A001109. a(n)=sqrt((A056854(n)^2 - 4)/45).

Second column of array A028412.

Cf. A049685.

Adjacent sequences: A004184 A004185 A004186 this_sequence A004188 A004189 A004190

Sequence in context: A124880 A081106 A036829 this_sequence A024092 A115589 A014390

nonn

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

Entry improved by comments from Michael Somos and Wolfdieter Lang (wolfdieter.lang(AT)physik.uni-karlsruhe.de), Aug 02 2000