login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A077849 Expansion of (1-x)^(-1)/(1 - 2*x - x^2 - x^3). 3

%I

%S 1,3,8,21,54,138,352,897,2285,5820,14823,37752,96148,244872,623645,

%T 1588311,4045140,10302237,26237926,66823230,170186624,433434405,

%U 1103878665,2811378360,7160069791,18235396608,46442241368,118279949136,301237536249,767197263003

%N Expansion of (1-x)^(-1)/(1 - 2*x - x^2 - x^3).

%H I. M. Gessel, Ji Li, <a href="https://cs.uwaterloo.ca/journals/JIS/VOL16/Gessel/gessel6.html">Compositions and Fibonacci identities</a>, J. Int. Seq. 16 (2013) 13.4.5

%H <a href="/index/Rec">Index entries for linear recurrences with constant coefficients</a>, signature (3,-1,0,-1)

%p A077939 := proc(n) if n< 0 then 0; else coeftayl( 1/(1-2*x-x^2-x^3) ,x=0,n) ; end if; end proc:

%p A077849 := proc(n) (-1+4*A077939(n)+2*A077939(n-1)+A077939(n-2))/3 ; end proc:

%p seq(A077849(n),n=0..20) ; # _R. J. Mathar_, Mar 22 2011

%t CoefficientList[Series[(1-x)^(-1)/(1-2x-x^2-x^3),{x,0,40}],x] (* or *) LinearRecurrence[{3,-1,0,-1},{1,3,8,21},40] (* _Harvey P. Dale_, Nov 01 2016 *)

%o (PARI) Vec((1-x)^(-1)/(1-2*x-x^2-x^3)+O(x^99)) \\ _Charles R Greathouse IV_, Sep 26 2012

%Y Partial sums of A077939.

%K nonn,easy

%O 0,2

%A _N. J. A. Sloane_, Nov 17 2002

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 July 12 19:34 EDT 2020. Contains 335668 sequences. (Running on oeis4.)