0,3

H. Brocard, Notes e'le'mentaires sur le proble`me de Peel, Nouvelles Correspondance Math\'{e}matique, 4 (1878), 161-169.

E. I. Emerson, Recurrent Sequences in the Equation DQ^2=R^2+N, Fib. Quart., 7 (1969), pps. 231-242.

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=8, 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=10.

T. D. Noe, Table of n, a(n) for n=0..100

Tanya Khovanova, Recursive Sequences

S. Plouffe, Approximations de S\'{e}ries G\'{e}n\'{e}ratrices et Quelques Conjectures}, Dissertation, Universit\'{e} du Qu\'{e}bec \`{a} Montr\'{e}al, 1992.

S. Plouffe, 1031 Generating Functions and Conjectures, Universit\'{e} du Qu\'{e}bec \`{a} Montr\'{e}al, 1992.

Index entries for sequences related to Chebyshev polynomials.

Zerinvary Lajos, Sage Notebooks

15*a(n)^2 - A001091(n)^2 = -1.

a(n) = S(2*n-1, sqrt(10))/sqrt(10) = S(n-1, 8); S(n, x) := U(n, x/2), Chebyshev polynomials of 2nd kind, A049310, with S(-1, x) := 0.

a(n)={{(4+sqrt(15))^n} - {(4-sqrt(15))^n}}/2*sqrt(15). G.f.(x)=x/(1-8x+x^2). - Barry E. Williams, Aug 18 2000

Lim. n-> Inf. a(n)/a(n-1) = 4 + sqrt(15). - Gregory V. Richardson (omomom(AT)hotmail.com), Oct 13 2002

a(n) = 7*(a(n-1)+a(n-2))-a(n-3). a(n) = 9*(a(n-1)-a(n-2))+a(n-3). - Mohamed Bouhamida (bhmd95(AT)yahoo.fr), Feb 07 2007

[A070997(n-1), a(n)] = [1,6; 1,7]^n * [1,0]. - Gary W. Adamson (qntmpkt(AT)yahoo.com), Mar 21 2008

a(-n) = -a(n). - Michael Somos Apr 05 2008

x + 8*x^2 + 63*x^3 + 496*x^4 + 3905*x^5 + 30744*x^6 + 242047*x^7 + ...

A001090:=1/(1-8*z+z**2); [S. Plouffe in his 1992 dissertation.]

(PARI) {a(n) = subst(poltchebi(n+1) - 4 * poltchebi(n), x, 4) / 15} /* Michael Somos Apr 05 2008 */

sage: [lucas_number1(n, 8, 1) for n in range(22)] - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Jun 25 2008

Cf. A000027, A001906, A001353, A004254, A001109, A004187, A001091.

a(n)=sqrt((A001091(n)^2-1)/15).

Cf. A070997.

Sequence in context: A080270 A085433 A081107 this_sequence A105219 A037205 A060071

Adjacent sequences: A001087 A001088 A001089 this_sequence A001091 A001092 A001093

nonn

njas

More terms from Wolfdieter Lang (wolfdieter.lang(AT)physik.uni-karlsruhe.de), Aug 02 2000