0,2

a(n) = L(n,-5)*(-1)^n, where L is defined as in A108299; see also A004253 for L(n,+5). - Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Jun 01 2005

General recurrence is a(n)=(a(1)-1)*a(n-1)-a(n-2), a(1)>=4, lim n->infinity a(n)= x*(k*x+1)^n, k =(a(1)-3), x=(1+sqrt((a(1)+1)/(a(1)-3)))/2. Examples in OEIS: a(1)=4 gives A002878, primes in it A121534. a(1)=5 gives A001834, primes in it A086386. a(1)=6 gives A030221, primes in it not in OEIS {29,139,3191,...}. a(1)=7 gives A002315, primes in it A088165. a(1)=8 gives A033890, primes in it not in OEIS (does there exist any ?). a(1)=9 gives A057080, primes in it not in OEIS {71,34649,16908641,...}. a(1)=10 gives A057081, primes in it not in OEIS {389806471,192097408520951,...}. [From Ctibor O. Zizka (ctibor.zizka(AT)seznam.cz), Sep 02 2008]

Inverse binomial transform of A030240. [From Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Nov 19 2009]

W. Lang, On polynomials related to powers of the generating function of Catalan's numbers, Fib. Quart. 38,5 (2000) 408-419; Eq.(44), rhs, m=6.

K. Dilcher and K. B. Stolarsky, A Pascal-type triangle characterizing twin primes, Amer. Math. Monthly, 112 (2005), 673-681. (see page 678)

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) = 5*a(n-1)-a(n-2), a(-1)=-1, a(0)=1; a(n)=U(2*n, sqrt(7)/2); g.f.: (1+x)/(x^2-5*x+1); a(n)=A004254(n)+A004254(n+1)

a(n) ~ (1/2 + 1/6*sqrt(21))*(1/2*(5 + sqrt(21)))^n - Joe Keane (jgk(AT)jgk.org), May 16 2002

Let q(n, x)=sum(i=0, n, x^(n-i)*binomial(2*n-i, i)); then (-1)^n*q(n, -7)=a(n) - Benoit Cloitre (benoit7848c(AT)orange.fr), Nov 10 2002

(Other) sage: [(lucas_number2(n, 5, 1)-lucas_number2(n-1, 5, 1))/3 for n in xrange(1, 22)]# [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Nov 10 2009]

Cf. A004253, A004254.

Sequence in context: A045445 A026884 A110311 this_sequence A009153 A012325 A125785

Adjacent sequences: A030218 A030219 A030220 this_sequence A030222 A030223 A030224

nonn

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