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

 

Logo

Please make a donation to keep the OEIS running. We are now in our 55th year. In the past year we added 12000 new sequences and reached 8000 citations (which often say "discovered thanks to the OEIS"). We need to raise money to hire someone to manage submissions, which would reduce the load on our editors and speed up editing.
Other ways to donate

Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A015447 Generalized Fibonacci numbers: a(n) = a(n-1) + 11*a(n-2). 21
1, 1, 12, 23, 155, 408, 2113, 6601, 29844, 102455, 430739, 1557744, 6295873, 23431057, 92685660, 350427287, 1369969547, 5224669704, 20294334721, 77765701465, 301003383396, 1156426099511, 4467463316867, 17188150411488 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

The compositions of n in which each positive integer is colored by one of p different colors are called p-colored compositions of n. For n>=2, 12*a(n-2) equals the number of 12-colored compositions of n, with all parts >= 2, such that no adjacent parts have the same color. - Milan Janjic, Nov 26 2011

LINKS

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

Index entries for linear recurrences with constant coefficients, signature (1,11).

FORMULA

a(n) = ( ( (1+3*sqrt(5))/2 )^(n+1) - ( (1-3*sqrt(5))/2 )^(n+1) )/3*sqrt(5).

a(n-1) = (1/3)*(-1)^n*Sum_{i=0..n} (-3)^i*Fibonacci(i)*C(n, i). - Benoit Cloitre, Mar 06 2004

a(n) = Sum_{k=0..n} A109466(n,k)*(-11)^(n-k). - Philippe Deléham, Oct 26 2008

G.f.: 1/(1 - x - 11*x^2). - Harvey P. Dale, May 08 2011

a(n) = ( Sum_{1<=k<=n+1, k odd} C(n+1,k)*45^((k-1)/2) )/2^n. - Vladimir Shevelev, Feb 05 2014

MATHEMATICA

Join[{a=1, b=1}, Table[c=b+11*a; a=b; b=c, {n, 100}]] (* Vladimir Joseph Stephan Orlovsky, Jan 16 2011 *)

LinearRecurrence[{1, 11}, {1, 1}, 30] (* or *) CoefficientList[Series[ 1/(1-x-11 x^2), {x, 0, 50}], x] (* Harvey P. Dale, May 08 2011 *)

PROG

(Sage) [lucas_number1(n, 1, -11) for n in xrange(0, 27)] # Zerinvary Lajos, Apr 22 2009

(MAGMA) [n le 2 select 1 else Self(n-1) + 11*Self(n-2): n in [1..30]]; // Vincenzo Librandi, Nov 06 2012

(PARI) Vec(1/(1-x-11*x^2)+O(x^99)) \\ Charles R Greathouse IV, Feb 03 2014

CROSSREFS

Cf. A015446, A015443.

Sequence in context: A083683 A294139 A255766 * A072822 A239656 A059161

Adjacent sequences:  A015444 A015445 A015446 * A015448 A015449 A015450

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
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified December 6 04:43 EST 2019. Contains 329784 sequences. (Running on oeis4.)