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

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A015454 Generalized Fibonacci numbers. 5
1, 1, 9, 73, 593, 4817, 39129, 317849, 2581921, 20973217, 170367657, 1383914473, 11241683441, 91317382001, 741780739449, 6025563297593, 48946287120193, 397595860259137, 3229713169193289, 26235301213805449, 213112122879636881 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

a(n)/a(n-1) tends to (8 + 2*sqrt(17))/2 = exp ArcSinh 4 = A176458. - Gary W. Adamson, Dec 26 2007

For n>=1, row sums of triangle for numbers 8^k*C(m,k) with duplicated diagonals. - Vladimir Shevelev, Apr 13 2012

For n>=1, a(n) equals the numbers of words of length n-1 on alphabet {0,1,...,8} containing no subwords ii, (i=0,1,...,7). - Milan Janjic, Jan 31 2015

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 0..1000

M. Janjic, On Linear Recurrence Equations Arising from Compositions of Positive Integers, 2014; http://matinf.pmfbl.org/wp-content/uploads/2015/01/za-arhiv-18.-1.pdf

Tanya Khovanova, Recursive Sequences

Index entries for linear recurrences with constant coefficients, signature (8,1)

FORMULA

a(n) = 8 a(n-1) + a(n-2).

a(n) = Sum_{k, 0<=k<=n}7^k*A055830(n,k). - Philippe Deléham, Oct 18 2006

G.f.: (1-7*x)/(1-8*x-x^2). [From Philippe Deléham, Nov 20 2008]

a(n) = (3/34)*sqrt(17)*[4-sqrt(17)]^n-(3/34)*[4+sqrt(17)]^n*sqrt(17)+(1/2)*[4+sqrt(17)]^n+(1/2) *[4-sqrt(17)]^n, with n>=0. [Paolo P. Lava, Nov 21 2008]

For n>=2, a(n)=F_n(8)+F_(n+1)(8), where F_n(x) is Fibonacci polynomial (cf.A049310): F_n(x)=sum{i=0,...,floor((n-1)/2)}C(n-i-1,i)x^(n-2*i-1). - Vladimir Shevelev, Apr 13 2012

a(n) = A041025(n) -7*A041025(n-1). - R. J. Mathar, Jul 06 2012

MATHEMATICA

LinearRecurrence[{8, 1}, {1, 1}, 30] (* Vincenzo Librandi, Nov 08 2012 *)

PROG

(MAGMA) [n le 2 select 1 else 8*Self(n-1) + Self(n-2): n in [1..30]]; // Vincenzo Librandi, Nov 08 2012

CROSSREFS

Sequence in context: A164588 A023001 A277672 * A121246 A086226 A199677

Adjacent sequences:  A015451 A015452 A015453 * A015455 A015456 A015457

KEYWORD

nonn,easy

AUTHOR

Olivier Gérard

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 25 13:25 EDT 2017. Contains 284080 sequences.