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

 

Logo

Annual Appeal: Today, Nov 11 2014, is the 4th anniversary of the launch of the new OEIS web site. 70,000 sequences have been added in these four years, all edited by volunteers. Please make a donation (tax deductible in the US) to help keep the OEIS running.

Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A097110 Expansion of (1+2*x-2*x^3)/(1-3*x^2+2*x^4). 2
1, 2, 3, 4, 7, 8, 15, 16, 31, 32, 63, 64, 127, 128, 255, 256, 511, 512, 1023, 1024, 2047, 2048, 4095, 4096, 8191, 8192, 16383, 16384, 32767, 32768, 65535, 65536, 131071, 131072, 262143, 262144, 524287, 524288, 1048575, 1048576, 2097151, 2097152 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

Union of A000079 and A000225 without 0 = 2^0 - 1. - Reinhard Zumkeller, Jan 18 2005

Let f(0)=1, f(1)=1, and f(n)=f(n-1-(1+(-1)^n)/2)+f(n-2); then a(n-1)=f(n). - John M. Campbell, May 22, 2011

LINKS

Table of n, a(n) for n=0..41.

Index to sequences with linear recurrences with constant coefficients, signature (0,3,0,-2).

FORMULA

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

a(n)=3*a(n-2)-2*a(n-4);

a(n)=(1+sqrt(2)/2)*(sqrt(2))^n+(1/2-sqrt(2)/2)*(-sqrt(2))^n-(1+(-1)^n)/2;

a(n)=sum(k=0..n, binomial(floor(n/2), floor(k/2)) ).

a(n) = 2^floor((n+2)/2) - 1 + n mod 2. - Reinhard Zumkeller, Jan 18 2005

MATHEMATICA

t={1}; Do[AppendTo[t, t[[-1]]+1]; AppendTo[t, t[[-1]]+t[[-2]]], {n, 10}]; t (* Vladimir Joseph Stephan Orlovsky, Jan 27 2012 *)

CoefficientList[Series[(1 + 2*x - 2*x^3)/(1 - 3*x^2 + 2*x^4), {x, 0, 40}], x] (* T. D. Noe, Jan 27 2012 *)

CROSSREFS

Sequence in context: A240690 A113050 A015927 * A116961 A120611 A092063

Adjacent sequences:  A097107 A097108 A097109 * A097111 A097112 A097113

KEYWORD

easy,nonn

AUTHOR

Paul Barry, Jul 25 2004, corrected Sep 05 2006

STATUS

approved

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

Content is available under The OEIS End-User License Agreement .

Last modified December 22 11:14 EST 2014. Contains 252355 sequences.