cp's OEIS Frontend

A193885 a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) - a(n-4), n>=4; a(0) = 1, a(1) = 1, a(2) = 2, a(3) = 3.

%I A193885 #20 Apr 07 2024 08:49:22
%S A193885 1,1,2,3,3,1,-5,-18,-41,-75,-115,-143,-118,35,431,1213,2499,4254,6047,
%T A193885 6665,3609,-7375,-32334,-77933,-147781,-234503,-305765,-283634,-20329,
%U A193885 718653,2239077,4824577,8495482,12533139,14698471,10166901,-9557053,-57006530
%N A193885 a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) - a(n-4), n>=4;  a(0) = 1, a(1) = 1, a(2) = 2, a(3) = 3.
%C A193885 The Ze1 sums, see A180662, of triangle A108299 equal the terms of this sequence.
%H A193885 Vincenzo Librandi, <a href="/A193885/b193885.txt">Table of n, a(n) for n = 0..1000</a>
%H A193885 <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (3,-3,1,-1).
%F A193885 a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) - a(n-4), n>=4; a(0) = 1, a(1) = 1, a(2) = 2, a(3) = 3.
%F A193885 G.f.: (1-x)*(1-x+x^2)/(1-3*x+3*x^2-x^3+x^4).
%F A193885 a(n) = (-1)^(n+1)*(A099531(n+4) + 2*A099531(n+3) + 2*A099531(n+2) + A099531(n+1)).
%p A193885 A193885 := proc(n) option remember: if n=0 then 1 elif n=1 then 1 elif n=2 then 2 elif n=3 then 3 elif n>=4 then 3*procname(n-1)-3*procname(n-2)+procname(n-3)-procname(n-4) fi: end: seq(A193885(n),n=0..37);
%t A193885 CoefficientList[Series[(1-x)*(1-x+x^2)/(1-3*x+3*x^2-x^3+x^4),{x,0,50}],x] (* _Vincenzo Librandi_, Jul 10 2012 *)
%o A193885 (Magma)I:=[1, 1, 2, 3 ]; [n le 4 select I[n] else 3*Self(n-1)-3*Self(n-2)+Self(n-3)-Self(n-4): n in [1..40]]; // _Vincenzo Librandi_, Jul 10 2012
%Y A193885 Cf. A099531, A108299, A180662.
%K A193885 sign,easy
%O A193885 0,3
%A A193885 _Johannes W. Meijer_, Aug 11 2011