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

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A015456 Generalized Fibonacci numbers. 5
1, 1, 11, 111, 1121, 11321, 114331, 1154631, 11660641, 117761041, 1189271051, 12010471551, 121293986561, 1224950337161, 12370797358171, 124932923918871, 1261700036546881, 12741933289387681, 128681032930423691, 1299552262593624591, 13124203658866669601 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

For n>=1, row sums of triangle for numbers 10^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,...,10} containing no subwords ii, (i=0,1,...,9). - 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 (10,1).

FORMULA

a(n) = 10 a(n-1) + a(n-2).

a(n) = Sum_{k, 0<=k<=n}9^k*A055830(n,k). - Philippe Deléham, Oct 18 2006

a(n) = (1/2)*[5+sqrt(26)]^n-(1/13)*[5+sqrt(26)]^n*sqrt(26)+(1/2)*[5-sqrt(26)]^n+(1/13)*sqrt(26) *[5-sqrt(26)]^n, with n>=0. - Paolo P. Lava, Jul 15 2008

G.f.: (1-9*x)/(1-10*x-x^2). [Philippe Deléham, Nov 20 2008]

For n>=2, a(n) = F_n(10)+F_(n+1)(10), 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

MATHEMATICA

LinearRecurrence[{10, 1}, {1, 1}, 30] (* Vincenzo Librandi, Nov 08 2012 *)

PROG

(MAGMA) [n le 2 select 1 else 10*Self(n-1) + Self(n-2): n in [1..30]]; // Vincenzo Librandi, Nov 08 2012

CROSSREFS

Sequence in context: A097115 A134732 A166747 * A240367 A199764 A097177

Adjacent sequences:  A015453 A015454 A015455 * A015457 A015458 A015459

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 May 23 07:01 EDT 2017. Contains 286909 sequences.