0,2

a(n) gives the general (positive integer) solution of the Pell equation b^2 - 165*a^2 =+4 with companion sequence b(n)=A078363(n+1), n>=0.

This is the m=15 member of the m-family of sequences S(n,m-2) = S(2*n+1,sqrt(m))/sqrt(m). The m=4..14 (nonnegative) sequences are: A000027, A001906, A001353, A004254, A001109, A004187, A001090, A018913, A004189, A004190 and A004191. The m=1..3 (signed) sequences are A049347, A056594, A010892.

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=13, 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=15.

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)=13*a(n-1)-a(n-2), n>= 1; a(-1)=0, a(0)=1.

a(n)=S(2*n+1, sqrt(15))/sqrt(15) = S(n, 13); S(n, x) := U(n, x/2), Chebyshev polynomials of the 2nd kind, A049310.

a(n)=(ap^(n+1)-am^(n+1))/(ap-am) with ap := (13+sqrt(165))/2 and am := (13-sqrt(165))/2.

G.f.: 1/(1-13*x+x^2).

sage: [lucas_number1(n, 13, 1) for n in xrange(1, 20)] - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Jun 25 2008

a(n)=sqrt((A078363(n+1)^2 - 4)/165), n>=0, (Pell equation d=165, +4).

Sequence in context: A087400 A012828 A119539 this_sequence A157381 A084970 A015961

Adjacent sequences: A078359 A078360 A078361 this_sequence A078363 A078364 A078365

nonn,easy

Wolfdieter Lang (wolfdieter.lang(AT)physik.uni-karlsruhe.de), Nov 29 2002