|
| |
|
|
A008998
|
|
a(n) = 2 a(n-1) + a(n-3).
|
|
11
| |
|
|
1, 2, 4, 9, 20, 44, 97, 214, 472, 1041, 2296, 5064, 11169, 24634, 54332, 119833, 264300, 582932, 1285697, 2835694, 6254320, 13794337, 30424368, 67103056, 148000449, 326425266, 719953588, 1587907625, 3502240516, 7724434620, 17036776865, 37575794246
(list; graph; refs; listen; history; internal format)
|
|
|
|
OFFSET
| 0,2
|
|
|
COMMENTS
| A transform of A000079 under the mapping mapping g(x)->(1/(1-x^3))g(x/(1-x^3)). - Paul Barry (pbarry(AT)wit.ie), Oct 20 2004
The binomial transform yields 1,3,9,..., i.e. A049220 without the leading zeros. - R. J. Mathar (mathar(AT)strw.leidenuniv.nl), May 15 2008
|
|
|
LINKS
| Vincenzo Librandi, Table of n, a(n) for n = 0..200
INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 452
B. Rittaud, On the Average Growth of Random Fibonacci Sequences, Journal of Integer Sequences, 10 (2007), Article 07.2.4.
Index to sequences with linear recurrences with constant coefficients, signature (2,0,1).
|
|
|
FORMULA
| a(n)=sum{k=0..floor(n/3), binomial(n-2k, k)2^(n-3k)} - Paul Barry (pbarry(AT)wit.ie), Oct 20 2004
O.g.f.: 1/(1-2x-x^3). - R. J. Mathar (mathar(AT)strw.leidenuniv.nl), May 15 2008
|
|
|
MAPLE
| A008998 := proc(n) option remember; if n <= 2 then 2^n else 2*A008998(n-1)+A008998(n-3); fi; end;
|
|
|
MATHEMATICA
| LinearRecurrence[{2, 0, 1}, {1, 2, 4}, 80] (* From Vladimir Joseph Stephan Orlovsky, Feb 13 2012 *)
|
|
|
PROG
| (MAGMA) [ n eq 1 select 1 else n eq 2 select 2 else n eq 3 select 4 else 2*Self(n-1)+Self(n-3): n in [1..40]]; // Vincenzo Librandi, Aug 21 2011
|
|
|
CROSSREFS
| Sequence in context: A129988 A035530 * A141016 A024736 A024562 A087219
Adjacent sequences: A008995 A008996 A008997 * A008999 A009000 A009001
|
|
|
KEYWORD
| nonn,easy,changed
|
|
|
AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com).
|
| |
|
|
