login
This site is supported by donations to The OEIS Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A052984 a(n) = 5*a(n-1) - 2*a(n-2) for n>1, with a(0) = 1, a(1) = 3. 10
1, 3, 13, 59, 269, 1227, 5597, 25531, 116461, 531243, 2423293, 11053979, 50423309, 230008587, 1049196317, 4785964411, 21831429421, 99585218283, 454263232573, 2072145726299, 9452202166349, 43116719379147, 196679192563037 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

a(n) = A020698(n) - 4*A020698(n-1) + 4*A020698(n-2) (n>=2). Kekulé numbers for certain benzenoids. - Emeric Deutsch, Jun 12 2005

REFERENCES

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

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 0..200

INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 1058

Index entries for linear recurrences with constant coefficients, signature (5,-2).

FORMULA

a(n) = A005824(2n).

G.f.: -(-1+2*x)/(1-5*x+2*x^2).

a(n) = Sum(1/17*(1+6*_alpha)*_alpha^(-1-n), _alpha=RootOf(1-5*_Z+2*_Z^2)).

a(k) = [M^k]_2,2, where M is the 3 X 3 matrix defined as follows: M = [2,1,2; 1,1,1; 2,1,2]. - Simone Severini, Jun 12 2006

a(n-1) = Sum_{k=0..n} A147703(n,k)*(-1)^k*2^(n-k), n>1. - Philippe Deléham, Nov 29 2008

a(n) = (a(n-1)^2 + 2^n)/a(n-2). - Irene Sermon, Oct 29 2013

MAPLE

spec := [S, {S=Sequence(Union(Prod(Sequence(Union(Z, Z)), Union(Z, Z)), Z))}, unlabeled ]: seq(combstruct[count ](spec, size=n), n=0..20);

a[0]:=1: a[1]:=3: for n from 2 to 25 do a[n]:=5*a[n-1]-2*a[n-2] od: seq(a[n], n=0..25); # Emeric Deutsch

MATHEMATICA

a[0] = 1; a[1] = 3; a[n_] := a[n] = 5a[n - 1] - 2a[n - 2]; Table[ a[n], {n, 0, 22}]

LinearRecurrence[{5, -2}, {1, 3}, 30] (* Harvey P. Dale, Apr 08 2014 *)

CoefficientList[Series[(1 - 2 x)/(1 - 5 x + 2 x^2), {x, 0, 40}], x] (* Vincenzo Librandi, Apr 09 2014 *)

PROG

(PARI) Vec((1-2*x)/(1-5*x+2*x^2)+O(x^99)) \\ Charles R Greathouse IV, Nov 20 2011

CROSSREFS

Cf. A005824, A020698.

Sequence in context: A268596 A199297 A152594 * A262664 A151229 A151230

Adjacent sequences:  A052981 A052982 A052983 * A052985 A052986 A052987

KEYWORD

nonn,easy

AUTHOR

encyclopedia(AT)pommard.inria.fr, Jan 25 2000

EXTENSIONS

Edited by Robert G. Wilson v, Dec 29 2002

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent | More pages
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy .

Last modified March 27 12:35 EDT 2017. Contains 284176 sequences.