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.

A019992 a(n) = 4*a(n-1) + a(n-2) - a(n-3) - a(n-5).

This page as a plain text file.
%I A019992 #24 Aug 20 2025 00:28:57
%S A019992 5,21,88,368,1538,6427,26857,112229,468978,1959746,8189306,34221135,
%T A019992 143001871,597570335,2497102330,10434788478,43604464772,182212543365,
%U A019992 761422279419,3181800093939,13295975323332,55560674643076,232174661258332,970201922073653,4054239874815929,16941690784755705,70795240417122020
%N A019992 a(n) = 4*a(n-1) + a(n-2) - a(n-3) - a(n-5).
%H A019992 Vincenzo Librandi, <a href="/A019992/b019992.txt">Table of n, a(n) for n = 0..1000</a>
%H A019992 <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (4,1,-1,0,-1).
%F A019992 G.f.: (5+x-x^2-x^4)/(1-4*x-x^2+x^3+x^5). - _Colin Barker_, Feb 21 2012
%t A019992 CoefficientList[Series[(5+x-x^2-x^4)/(1-4*x-x^2+x^3+x^5),{x,0,30}],x] (* _Vincenzo Librandi_, Apr 20 2012 *)
%t A019992 LinearRecurrence[{4,1,-1,0,-1},{5,21,88,368,1538},30] (* _Harvey P. Dale_, May 03 2020 *)
%o A019992 (Magma) I:=[5, 21, 88, 368, 1538]; [n le 5 select I[n] else 4*Self(n-1)+Self(n-2)-Self(n-3)-Self(n-5): n in [1..30]]; // _Vincenzo Librandi_, Apr 20 2012
%Y A019992 This is different from A010925. See the comments in that sequence.
%K A019992 nonn,easy
%O A019992 0,1
%A A019992 _R. K. Guy_
%E A019992 More terms from Pab Ter (pabrlos(AT)yahoo.com), May 23 2004