0,2

Number of words of length n without adjacent 0's from the alphabet {0,1,2}. For example, a(2) counts 01,02,10,11,12,20,21,22. - Antonio G. Astudillo (afg_astudillo(AT)hotmail.com), Jun 12 2001

Individually, both this sequence and A002605 are convergents to 1+sqrt(3). Mutually, both sequences are convergents to 2+sqrt(3) and 1+sqrt(3)/2.- Klaus E. Kastberg (kastberg(AT)hotkey.net.au), Nov 04 2001

Add a loop at two vertices of the graph C_3=K_3. A028859(n) counts walks of length n+1 between these vertices. - Paul Barry (pbarry(AT)wit.ie), Oct 15 2004

Contribution from Gary W. Adamson (qntmpkt(AT)yahoo.com), Jul 28 2009: (Start)

Prefaced with a 1 as (1 + x + 3x^2 + 8x^3 + 22x^4 + ...) =

1 / (1 - x - 2x^2 - 3x^3 - 5x^4 - 8x^5 - 13x^6 - 21x^7 - ...). (End)

S. J. Cyvin and I. Gutman, Kekule structures in benzenoid hydrocarbons, Lecture Notes in Chemistry, No. 46, Springer, New York, 1988 (see p. 73).

David Garth and Adam Gouge, Affinely Self-Generating Sets and Morphisms, Journal of Integer Sequences, Vol. 10 (2007), Article 07.1.5.

Index entries for sequences related to linear recurrences with constant coefficients

Joerg Arndt, Fxtbook

Tanya Khovanova, Recursive Sequences

a(n) = a(n-1) + A052945(n) = A002605(n) + A002605(n-1); generating function = -(x+1)/(2*x^2+2*x-1).

a(n)=[(1+sqrt(3))^(n+2)-(1-sqrt(3))^(n+2)]/(4sqrt(3)). - Emeric Deutsch (deutsch(AT)duke.poly.edu), Feb 01 2005

a[0]:=1:a[1]:=3:for n from 2 to 24 do a[n]:=2*a[n-1]+2*a[n-2] od: seq(a[n], n=0..24); (Deutsch)

Sequence in context: A077848 A055887 A024581 this_sequence A155020 A014397 A048503

Adjacent sequences: A028856 A028857 A028858 this_sequence A028860 A028861 A028862

nonn

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