0,2

The even neighbor must differ from the odd number by exactly one.

If we defined this sequence by the recurrence (a(n) = 3*a(n-1) + 2*a(n-2)) that it satisfies, we could prefix it with an initial 0.

a(n) equals term (1,2) in M^n, M = the 3x3 matrix [1,1,2; 1,0,1; 2,1,1]. [From Gary W. Adamson (qntmpkt(AT)yahoo.com), Mar 12 2009]

a(n) equals term (2,2) in M^n, M = the 3x3 matrix [0,1,0; 1,3,1; 0,1,0]. [From Paul Barry (pbarry(AT)wit.ie), Sep 18 2009]

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

R. K. Guy, Moser, William O.J.: Numbers of subsequences without isolated odd members. Fibonacci Quarterly, 34, No. 2, 152-155 (1996). Math. Rev. 97d:11017.

T. D. Noe, Table of n, a(n) for n=0..200

INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 442

Let b(0)=1, b(k)=floor(b(k-1))+2/b(k-1); then, for n>0, b(n)=a(n)/a(n-1). - Benoit Cloitre (benoit7848c(AT)orange.fr), Sep 09 2002

The Hankel transform of this sequence is [1,2,0,0,0,0,0,0,0,...]. - Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Nov 21 2007

G.f.: 1/(1-3x-2x^2). a(n)=3a(n-1)+2a(n-2). a(n)=(ap^(n+1)-am^(n+1))/(ap-am), ap := (3+sqrt(17))/2, am := (3-sqrt(17))/2.

a(n)=sum{k=0..floor(n/2), C(n-k, k)2^k*3^(n-2k)} - Paul Barry (pbarry(AT)wit.ie), Apr 23 2005

a(n)=Sum_{k, 0<=k<=n}A112906(n,k). - Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Nov 21 2007

(Other) sage: [lucas_number1(n, 3, -2) for n in xrange(1, 25)] # [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Apr 22 2009]

Cf. A007455, A007481, A007483, A007484.

Row sums of triangle A073387.

Cf. A000045, A000129, A001045.

Adjacent sequences: A007479 A007480 A007481 this_sequence A007483 A007484 A007485

Sequence in context: A089579 A166336 A002783 this_sequence A134760 A132889 A149061

nonn,easy,nice

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