0,5

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

Row sums of Riordan array (1/(1+2x^2),x/(1+2x^2)). - Paul Barry (pbarry(AT)wit.ie), Sep 10 2005

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

Eric Weisstein's World of Mathematics, Lehmer Number

G.f.; x/(1-x+2x^2). a(n)=a(n-1)-2*a(n-2).

a(n+1)=sum{k=0..n, C((n+k)/2, k)*(-2)^((n-k)/2)*(1+(-1)^(n-k))/2}; a(n+1)=sum{k=0..floor(n/2), C(n-k, k)(-2)^k}; - Paul Barry (pbarry(AT)wit.ie), Sep 10 2005

a(n+1)=Sum_{k, 0<=k<=n} A109466(n,k)*2^(n-k). [From Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Oct 26 2008]

a:= n-> (Matrix([[1, 1], [ -2, 0]])^n)[1, 2]: seq (a(n), n=0..45); [From Alois P. Heinz (heinz(AT)hs-heilbronn.de), Sep 03 2008]

(PARI) a(n)=if(n<0, 0, imag(quadgen(-7)^n))

(Other) sage: [lucas_number1(n, 1, +2) for n in xrange(0, 46)] # [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Apr 22 2009]

A001607(n)=-(-1)^n*a(n).

Sequence in context: A001607 A167433 A077020 this_sequence A159285 A021080 A049764

Adjacent sequences: A107917 A107918 A107919 this_sequence A107921 A107922 A107923

sign

Michael Somos, May 28 2005