0,5

x/(x^2+x+2)=sum(n=0,inf,a(n)*(x/2)^n) - Benoit Cloitre (benoit7848c(AT)orange.fr), Mar 12 2002

4*2^n = A002249(n)^2+7*A001607(n)^2. See A077020, A077021.

Apart from the sign, this is an example of a sequence of Lehmer numbers. In this case, the two parameters, alpha and beta, are (1 +- i Sqrt(7))/2. Bilu, Hanrot, Voutier and Mignotte show that all terms of a Lehmer sequence a(n) have a primitive factor for n > 30. Note that for this sequence, a(30) = 24475 = 5*5*11*89 has no primitive factors. - T. D. Noe (noe(AT)sspectra.com), Oct 29 2003

D. Jarden, Recurring Sequences. Riveon Lematematika, Jerusalem, 1966.

Erwin Just, Problem E2367, Amer. Math. Monthly, 79 (1972), 772.

N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).

N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

Y. Bilu, G. Hanrot, P. M. Voutier and M. Mignotte, Existence of primitive divisors of Lucas and Lehmer numbers

G. P. Michon, Never Back to -1.

Eric Weisstein's World of Mathematics, Lehmer Number

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

a(n) = Sum_{k=0..n-1} (-1)^(n-k-1)*binomial(n-k-1, k)*2^k = -2/sqrt(7)*(-sqrt(2))^n*(sin(n*arctan(sqrt(7)))). - Vladeta Jovovic (vladeta(AT)eunet.rs), Feb 05 2003

(PARI) a(n)=if(n<0, 0, polcoeff(x/(1+x+2*x^2)+x*O(x^n), n))

(PARI) a(n)=if(n<0, 0, 2*imag(((-1+quadgen(-28))/2)^n))

Apart from signs, same as A077020.

Sequence in context: A038871 A143524 A134249 this_sequence A167433 A077020 A107920

Adjacent sequences: A001604 A001605 A001606 this_sequence A001608 A001609 A001610

sign,easy

N. J. A. Sloane (njas(AT)research.att.com).