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 A215205 #20 Feb 17 2024 12:35:02
%S A215205 1,-2,4,-4,6,-8,10,-9,11,-14,16,-14,16,-20,22,-19,21,-26,28,-24,26,
%T A215205 -32,34,-29,31,-38,40,-34,36,-44,46,-39,41,-50,52,-44,46,-56,58,-49,
%U A215205 51,-62,64,-54,56,-68,70,-59,61,-74,76,-64,66,-80,82,-69,71,-86,88,-74,76,-92,94,-79,81,-98,100,-84
%N A215205 a(n) = (-1)^n * (A060819(n) + A060819(n+1)).
%C A215205 a(-1)=1=a(0).
%C A215205 a(n) - a(n-1) = b(n) = 0, -3, 6, -8, 10, -14, 18, -19, 20, -25, 30, -30, 30, -36, 42, -41, ... .
%C A215205 Missing terms in abs(a(n)):
%C A215205 PIII(n) = 0, 3, 5, 7, 12, 13, 15, 17, 18, 23, 25, 27, 30, 33, 35, 37, 42, ... . See A063241(n+1) and 6*A047222(n+1).
%C A215205 Quasipolynomial of order 4. - _Charles R Greathouse IV_, Aug 06 2012
%H A215205 <a href="/index/Rec#order_07">Index entries for linear recurrences with constant coefficients</a>, signature (-1,-1,-1,1,1,1,1).
%F A215205 a(4*n) = 1+5*n, a(1+4*n) = -2-6*n, a(2+4*n) = 4+6*n, a(3+4*n) = -4-5*n.
%F A215205 a(n+4) - a(n) = period of length 4: repeat 5,-6, 6, -5.
%F A215205 a(n) = 2*a(n-4) + a(n-8).
%F A215205 G.f. ( -1+x-3*x^2-3*x^4+x^3+x^5-x^6 ) / ( (x-1)*(1+x)^2*(x^2+1)^2 ). - _R. J. Mathar_, Aug 07 2012
%F A215205 a(n) = (5+(2*n+1)*(11*(-1)^n-(-1)^((2*n-1+(-1)^n)/4))+(-1)^((6*n-1 +(-1)^n)/4))/16. - _Luce ETIENNE_, Jun 05 2015
%t A215205 a[n_] := Switch[Mod[n, 4], 0, 5n/4+1, 1, (-3n-1)/2, 2, 3n/2+1, 3, (-5n-1)/4]; Table[a[n], {n, 0, 67}] (* _Jean-François Alcover_, Nov 08 2012 *)
%Y A215205 Cf. A016861, A016933, A016957, A016897.
%K A215205 sign,less,easy
%O A215205 0,2
%A A215205 _Paul Curtz_, Aug 06 2012