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.
%I A215898 #51 Feb 17 2024 06:28:15
%S A215898 1,-2,4,-3,5,-8,10,-7,9,-14,16,-11,13,-20,22,-15,17,-26,28,-19,21,-32,
%T A215898 34,-23,25,-38,40,-27,29,-44,46,-31,33,-50,52,-35,37,-56,58,-39,41,
%U A215898 -62,64,-43,45,-68,70,-47,49,-74,76,-51,53,-80,82,-55,57,-86,88,-59
%N A215898 a(4n) = 1+4n, a(1+4n) = -2-6n, a(2+4n) = 4+6n, a(3+4n) = -3-4n.
%C A215898 A permutation of A047253, numbers that are not divisible by 6.
%H A215898 Bruno Berselli, <a href="/A215898/b215898.txt">Table of n, a(n) for n = 0..1000</a>
%H A215898 <a href="/index/Rec#order_07">Index entries for linear recurrences with constant coefficients</a>, signature (-1,-1,-1,1,1,1,1).
%F A215898 a(n) = 2*a(n-4) - a(n-8).
%F A215898 a(2*n) + a(1+2*n) = -A109613(n)*(-1)^n.
%F A215898 a(3*n) + a(1+3*n) + a(2+3*n) = 3*a(n).
%F A215898 a(4*n) + a(1+4*n) + a(2+4*n) + a(3+4*n) = 0.
%F A215898 a(5*n) + a(1+5*n) + a(2+5*n) + a(3+5*n) + a(4+5*n) = 5*a(n).
%F A215898 From _Bruno Berselli_, Sep 07 2012: (Start)
%F A215898 G.f.: (1-x+3*x^2+3*x^4-x^5+x^6)/((1-x)*(1+x+x^2+x^3)^2).
%F A215898 a(n) = 1+(5-i^(n*(n+1)))*((2*n+1)*(-1)^n-1)/8, where i=sqrt(-1).
%F A215898 a(2*n) = 1+(5-(-1)^n)*n/2; a(2*n+1) = 1-(5+(-1)^n)*(n+1)/2.
%F A215898 a(n) = a(-n-1) = -a(n-1)-a(n-2)-a(n-3)+a(n-4)+a(n-5)+a(n-6)+a(n-7). (End)
%t A215898 a[n_ /; Mod[n, 4] == 0] := n+1; a[n_ /; Mod[n, 4] == 1] := -(3n+1)/2; a[n_ /; Mod[n, 4] == 2] := (3n+2)/2; a[n_ /; Mod[n, 4] == 3] := -n; Table[a[n], {n, 0, 70}] (* _Jean-François Alcover_, Sep 03 2012 *)
%t A215898 LinearRecurrence[{-1,-1,-1,1,1,1,1},{1,-2,4,-3,5,-8,10},60] (* _Harvey P. Dale_, Mar 24 2023 *)
%o A215898 (Magma) m:=60; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!((1-x+3*x^2+3*x^4-x^5+x^6)/((1-x)*(1+x+x^2+x^3)^2))); // _Bruno Berselli_, Sep 06 2012
%o A215898 (Maxima) makelist(expand(1+(5-%i^(n*(n+1)))*((2*n+1)*(-1)^n-1)/8), n, 0, 60); /* _Bruno Berselli_, Sep 07 2012 */
%Y A215898 Cf. A016813, A016933, A016957, A004767.
%K A215898 sign,easy
%O A215898 0,2
%A A215898 _Paul Curtz_, Aug 25 2012