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

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A114697 Expansion of (1+x+x^2)/((x-1)*(x+1)*(x^2+2*x-1)); a Pellian-related sequence. 5

%I

%S 1,3,9,22,55,133,323,780,1885,4551,10989,26530,64051,154633,373319,

%T 901272,2175865,5253003,12681873,30616750,73915375,178447501,

%U 430810379,1040068260,2510946901,6061962063,14634871029,35331704122,85298279275,205928262673

%N Expansion of (1+x+x^2)/((x-1)*(x+1)*(x^2+2*x-1)); a Pellian-related sequence.

%C Generating floretion: (- .5'j + .5'k - .5j' + .5k' + 'ii' - .5'ij' - .5'ik' - .5'ji' - .5'ki')*('i + 'j + i')

%H Colin Barker, <a href="/A114697/b114697.txt">Table of n, a(n) for n = 0..1000</a>

%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (2,2,-2,-1).

%F a(n+2) - 2*a(n+1) + a(n) = A111955(n+2).

%F a(2*n) = A216134(2*n+1). a(2*n+1) = A006452(2*n+3)-1. Lim a(n+1)/a(n) = A014176. - _Raphie Frank_, Oct 01 2012

%F a(n) = A078343(n+2)/2 - A010694(n)/4. - _R. J. Mathar_, Oct 02 2012

%F From _Colin Barker_, May 26 2016: (Start)

%F a(n) = (2*(-3+(-1)^n)+(6-5*sqrt(2))*(1-sqrt(2))^n+(1+sqrt(2))^n*(6+5*sqrt(2)))/8.

%F a(n) = 2*a(n-1)+2*a(n-2)-2*a(n-3)-a(n-4) for n>3.

%F (End)

%o (PARI) Vec((x^2+x+1)/((x-1)*(x+1)*(x^2+2*x-1)) + O(x^100)) \\ _Colin Barker_, Jun 24 2015

%Y Cf. A100828, A111954, A113224, A114647, A114688, A114689, A114695, A116699, A000129, A005409.

%K easy,nonn

%O 0,2

%A _Creighton Dement_, Feb 18 2006

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 November 20 18:21 EST 2019. Contains 329337 sequences. (Running on oeis4.)