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!)
A016801 Expansion of 1/((1-3x)(1-4x)(1-7x)). 2

%I #20 Sep 08 2022 08:44:41

%S 1,14,135,1120,8621,63714,460195,3280340,23204841,163423414,

%T 1147981055,8052113160,56430306661,395275799114,2767989986715,

%U 19380181827580,135678323522081,949816596710814,6648989892621175

%N Expansion of 1/((1-3x)(1-4x)(1-7x)).

%H Harvey P. Dale, <a href="/A016801/b016801.txt">Table of n, a(n) for n = 0..1000</a>

%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (14, -61, 84).

%F a(n) = 14*a(n-1) - 61*a(n-2) + 84*a(n-3); a(0)=1, a(1)=14, a(2)=135. - _Harvey P. Dale_, May 10 2012

%F a(n) = 9*3^n/4 - 16*4^n/3 + 49*7^n/12. - _R. J. Mathar_, Jun 23 2013

%F a(n) = 11*a(n-1) - 28*a(n-2) + 3^n. - _Vincenzo Librandi_, Jun 26 2013

%t CoefficientList[Series[1/((1-3x)(1-4x)(1-7x)),{x,0,20}],x] (* or *) LinearRecurrence[{14,-61,84},{1,14,135},20] (* _Harvey P. Dale_, May 10 2012 *)

%o (PARI) Vec(1/((1-3*x)*(1-4*x)*(1-7*x))+O(x^99)) \\ _Charles R Greathouse IV_, Sep 26 2012

%o (Magma) I:=[1, 14, 135]; [n le 3 select I[n] else 14*Self(n-1)-61*Self(n-2)+84*Self(n-3): n in [1..20]]; /* or */ m:=20; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!((1/((1-3*x)*(1-4*x)*(1-7*x))))); // _Vincenzo Librandi_, Jun 26 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 06:57 EDT 2024. Contains 371265 sequences. (Running on oeis4.)