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.

A154595 Period 6: repeat [1, 3, 3, -1, -3, -3].

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%I A154595 #19 Dec 12 2023 08:02:50
%S A154595 1,3,3,-1,-3,-3,1,3,3,-1,-3,-3,1,3,3,-1,-3,-3,1,3,3,-1,-3,-3,1,3,3,-1,
%T A154595 -3,-3,1,3,3,-1,-3,-3,1,3,3,-1,-3,-3,1,3,3,-1,-3,-3,1,3,3,-1,-3,-3,1,
%U A154595 3,3,-1,-3,-3,1,3,3,-1,-3,-3,1,3,3,-1,-3,-3,1,3
%N A154595 Period 6: repeat [1, 3, 3, -1, -3, -3].
%C A154595 First differences of A154127.
%H A154595 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (0,0,-1).
%F A154595 G.f.: ( 1+3*x+3*x^2 ) / ( (1+x)*(x^2-x+1) ). - _R. J. Mathar_, Dec 04 2011
%F A154595 From _Wesley Ivan Hurt_, Jun 23 2016: (Start)
%F A154595 a(n) + a(n-3) = 0 for n>2.
%F A154595 a(n) = (cos(n*Pi) + 2*cos(n*Pi/3) + 6*sqrt(3)*sin(n*Pi/3))/3. (End)
%p A154595 A154595:=n->[1, 3, 3, -1, -3, -3][(n mod 6)+1]: seq(A154595(n), n=0..100); # _Wesley Ivan Hurt_, Jun 23 2016
%t A154595 PadRight[{}, 120, {1,3,3,-1,-3,-3}] (* _Harvey P. Dale_, Aug 09 2013 *)
%o A154595 (Magma) &cat [[1, 3, 3, -1, -3, -3]^^20]; // _Wesley Ivan Hurt_, Jun 23 2016
%Y A154595 Cf. A154127.
%K A154595 sign,easy
%O A154595 0,2
%A A154595 _Paul Curtz_, Jan 12 2009
%E A154595 Edited by _N. J. A. Sloane_, Jan 12 2009