0,1

Satisfies (a(n))^2 = a(2n) + 2. Shifted differences of itself.

Multiplicative with a(2^e) = -1, a(3^e) = -2, a(p^e) = 1 otherwise. David W. Wilson (davidwwilson(AT)comcast.net) Jun 12, 2005.

A. T. Benjamin and J. J. Quinn, Proofs that really count: the art of combinatorial proof, M.A.A. 2003, id. 176.

Tanya Khovanova, Recursive Sequences

Index entries for recurrences a(n) = k*a(n - 1) +/- a(n - 2)

a(n) = a(n-1) - a(n-2), starting with a(0) = 2 and a(1) = 1.

G.f.: (2-x)/(1-x+x^2). a(n) = Sum[k>=0, (-1)^k*n/(n-k)*C(n-k, k) ].

a(n) = (1/2) {(-1)^[n/3] + 2(-1)^[(n+1)/3] + (-1)^[(n+2)/3] }.

a(n)=-(1/6)*[n mod 6+2*((n+1) mod 6)+(n+2) mod 6-(n+3) mod 6-2*((n+4) mod 6)-(n+5) mod 6] - Paolo P. Lava (ppl(AT)spl.at), Oct 09 2006

Moebius transform is length 6 sequence [ 1, -2, -3, 0, 0, 6]. - Michael Somos Oct 22 2006

a(n)=a(-n)=-a(n-3). - Michael Somos Oct 22 2006

a(2) = -1 = a(1) - a(0) = 1 - 2 = ((1+sqrt(-3))/2)^2 + ((1-sqrt(-3))/2)^2 = -1 = -2/4 + 2sqrt(-3)/4 - 2/4 -2 sqrt(-3)/4 = -1.

(PARI) {a(n)=[2, 1, -1, -2, -1, 1][n%6+1]} /* Michael Somos Oct 22 2006 */

(Other) sage: [lucas_number2(n, 1, 1) for n in xrange(0, 102)]# [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Apr 30 2009]

Essentially the same as A057079 and A100051. Pairwise sums of A010892.

Adjacent sequences: A087201 A087202 A087203 this_sequence A087205 A087206 A087207

Sequence in context: A132367 A101825 A057079 this_sequence A131534 A061347 A115579

easy,sign,mult

Nikolay V. Kosinov (kosinov(AT)unitron.com.ua), Oct 19 2003

Edited by Ralf Stephan, Feb 04 2005