cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

A020000 Expansion of 1/((1-5*x)*(1-7*x)*(1-11*x)).

This page as a plain text file.
%I A020000 #23 May 09 2025 13:38:17
%S A020000 1,23,362,4870,60411,715533,8243572,93366380,1046230421,11644889443,
%T A020000 129058033182,1426436938290,15738640474831,173461105001753,
%U A020000 1910430676985192,21031277618176600,231459987587209641
%N A020000 Expansion of 1/((1-5*x)*(1-7*x)*(1-11*x)).
%H A020000 Vincenzo Librandi, <a href="/A020000/b020000.txt">Table of n, a(n) for n = 0..200</a>
%H A020000 <a href="/index/Rec">Index entries for linear recurrences with constant coefficients</a>, signature (23,-167,385)
%F A020000 a(n) = 5^(n+2)/12+11^(n+2)/24-7^(n+2)/8. - R. J. Mathar, Mar 15 2011
%F A020000 a(0)=1, a(1)=23, a(2)=362; for n>2, a(n) = 23*a(n-1) -167*a(n-2) +385*a(n-3). - _Vincenzo Librandi_, Jul 03 2013
%F A020000 a(n) = 18*a(n-1) -77*a(n-2) +5^n. - _Vincenzo Librandi_, Jul 03 2013
%t A020000 CoefficientList[Series[1 / ((1 - 5 x) (1 - 7 x) (1 - 11 x)), {x, 0, 20}], x] (* _Vincenzo Librandi_, Jul 03 2013 *)
%t A020000 LinearRecurrence[{23,-167,385},{1,23,362},20] (* _Harvey P. Dale_, May 09 2025 *)
%o A020000 (PARI) Vec(1/((1-5*x)*(1-7*x)*(1-11*x))+O(x^99)) \\ _Charles R Greathouse IV_, Sep 26 2012
%o A020000 (Magma) m:=20; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!(1/((1-5*x)*(1-7*x)*(1-11*x)))); // _Vincenzo Librandi_, Jul 03 2013
%o A020000 (Magma) I:=[1, 23, 362]; [n le 3 select I[n] else 23*Self(n-1)-167*Self(n-2)+385*Self(n-3): n in [1..20]]; // _Vincenzo Librandi_, Jul 03 2013
%K A020000 nonn,easy
%O A020000 0,2
%A A020000 _N. J. A. Sloane_