cp's OEIS Frontend

A065262 The nonpositive side (-1, -2, -3, ...) of the site swap sequence A065261. The bisection of odd terms of A065261.

%I A065262 #23 Sep 08 2022 08:45:04
%S A065262 1,1,5,2,9,3,13,4,17,5,21,6,25,7,29,8,33,9,37,10,41,11,45,12,49,13,53,
%T A065262 14,57,15,61,16,65,17,69,18,73,19,77,20,81,21,85,22,89,23,93,24,97,25,
%U A065262 101,26,105,27,109,28,113,29,117,30,121,31,125,32,129,33,133,34,137,35
%N A065262 The nonpositive side (-1, -2, -3, ...) of the site swap sequence A065261. The bisection of odd terms of A065261.
%H A065262 Colin Barker, <a href="/A065262/b065262.txt">Table of n, a(n) for n = 1..1000</a>
%H A065262 <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (0,2,0,-1).
%F A065262 G.f.: x*(3*x^2+x+1) / ((x-1)^2*(x+1)^2). [_Colin Barker_, Feb 18 2013]
%F A065262 From _Wesley Ivan Hurt_, Dec 06 2015: (Start)
%F A065262 a(n) = 2*a(n-2)-a(n-4) for n>4.
%F A065262 a(n) = n - Sum_{i=1..n} ceiling( (-1)^i*(2*n-3+i)/2 ). (End)
%p A065262 a:=proc(n) option remember; if n=1 then 1 elif n=2 then 1 elif n=3 then 5 elif n=4 then 2 else 2*a(n-2)-a(n-4); fi; end:  seq(a(n), n=1..100); # _Wesley Ivan Hurt_, Dec 06 2015
%t A065262 CoefficientList[Series[(3*x^2 + x + 1)/(x^2 - 1)^2, {x, 0, 100}], x] (* or *) LinearRecurrence[{0, 2, 0, -1}, {1, 1, 5, 2}, 100] (* _Wesley Ivan Hurt_, Dec 06 2015 *)
%o A065262 (PARI) Vec(x*(3*x^2+x+1) / ((x-1)^2*(x+1)^2) + O(x^100)) \\ _Michel Marcus_, Dec 06 2015
%o A065262 (PARI) vector(100, n, n - sum(i=1, n, ceil((-1)^i*(2*n-3+i)/2 ))) \\ _Altug Alkan_, Dec 06 2015
%o A065262 (Magma) I:=[1, 1, 5, 2]; [n le 4 select I[n] else 2*Self(n-2)-Self(n-4) : n in [1..100]]; // _Wesley Ivan Hurt_, Dec 06 2015
%Y A065262 Cf. A065261.
%K A065262 nonn,easy
%O A065262 1,3
%A A065262 _Antti Karttunen_, Oct 28 2001