0,2

a(n)=A020698(n)-2*A020698(n-1) (n>=1). Kekule numbers for certain benzenoids.

This is the number of spanning, connected subgraphs of the "ladder graph" of n squares (ladder graph = the vertices and edges of the tiling of a 1 x n rectangle by unit squares). - David Pasino (davepasino(AT)yahoo.com), Sep 18 2007

S. J. Cyvin and I. Gutman, Kekule structures in benzenoid hydrocarbons, Lecture Notes in Chemistry, No. 46, Springer, New York, 1988 (see p. 78).

a(n)=5a(n-1)=2a(n-2), a(0)=1, a(1)=5.

a(k) = [M^k]_1,2, where M is the 3 by 3 matrix defined as follows: M = [2,1,2;1,1,1;2,1,2]. - Simone Severini (ss54(AT)york.ac.uk), Jun 12 2006

a(n) = (((5 + s)/2)^(n+1) - ((5 - s)/2)^(n+1))/s with s = 17^(1/2) [From David Pasino (davepasino(AT)yahoo.com), Jan 09 2009]

G.f.: 1/(1-5*x+2*x^2). [From R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Apr 07 2009]

sage: [lucas_number1(n, 5, 2) for n in range(27)] - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Jun 25 2008

(Other) sage: [lucas_number1(n, 5, 2) for n in xrange(1, 24)]# [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Apr 22 2009]

Cf. A020698.

Sequence in context: A167660 A026760 A064914 this_sequence A128732 A026894 A126473

Adjacent sequences: A107836 A107837 A107838 this_sequence A107840 A107841 A107842

nonn

Emeric Deutsch (deutsch(AT)duke.poly.edu), Jun 12 2005