login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A018070 Expansion of 1/((1-3x)(1-8x)(1-11x)). 1

%I #21 Sep 08 2022 08:44:44

%S 1,22,339,4532,56357,672210,7813303,89300464,1009144713,11315328398,

%T 126186563867,1401795991596,15529706751469,171706382611786,

%U 1895807080277631,20910172869786728,230462261504563025

%N Expansion of 1/((1-3x)(1-8x)(1-11x)).

%H Vincenzo Librandi, <a href="/A018070/b018070.txt">Table of n, a(n) for n = 0..200</a>

%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (22,-145,264).

%F a(n) = 22*a(n-1) - 145*a(n-2) + 264*a(n-3) for n>2; a(0)=1, a(1)=22, a(2)=339. - _Vincenzo Librandi_, Jul 02 2013

%F a(n) = 19*a(n-1) - 88*a(n-2) + 3^n. - _Vincenzo Librandi_, Jul 02 2013

%F a(n) = (5*11^(n+2) - 8^(n+3) + 3^(n+3))/120. - _Yahia Kahloune_, Jul 06 2013

%t CoefficientList[Series[1 / ((1 - 3 x) (1 - 8 x) (1 - 11 x)), {x, 0, 30}], x] (* _Vincenzo Librandi_, Jul 02 2013 *)

%t LinearRecurrence[{22,-145,264},{1,22,339},30] (* _Harvey P. Dale_, Jan 22 2014 *)

%o (Magma) m:=20; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!(1/((1-3*x)*(1-8*x)*(1-11*x)))); /* or */ I:=[1, 22, 339]; [n le 3 select I[n] else 22*Self(n-1)-145*Self(n-2)+264*Self(n-3): n in [1..20]]; // _Vincenzo Librandi_, Jul 02 2013

%K nonn,easy

%O 0,2

%A _N. J. A. Sloane_

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

License Agreements, Terms of Use, Privacy Policy. .

Last modified March 29 07:27 EDT 2024. Contains 371265 sequences. (Running on oeis4.)