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A168309 Period 2: repeat 4,-3.

%I A168309 #17 Sep 08 2022 08:45:49
%S A168309 4,-3,4,-3,4,-3,4,-3,4,-3,4,-3,4,-3,4,-3,4,-3,4,-3,4,-3,4,-3,4,-3,4,
%T A168309 -3,4,-3,4,-3,4,-3,4,-3,4,-3,4,-3,4,-3,4,-3,4,-3,4,-3,4,-3,4,-3,4,-3,
%U A168309 4,-3,4,-3,4,-3,4,-3,4,-3,4,-3,4,-3,4,-3,4,-3,4,-3,4,-3,4,-3,4,-3,4,-3,4,-3
%N A168309 Period 2: repeat 4,-3.
%C A168309 Interleaving of A010709 and -3*A000012.
%C A168309 Binomial transform of 4 followed by a signed version of A005009.
%C A168309 Inverse binomial transform of 4 followed by A000079.
%C A168309 a(n+1) - a(n) = 7*(-1)^n.
%C A168309 A168230 without initial term 0 gives partial sums.
%C A168309 Nonsimple continued fraction expansion of 2+2*sqrt(2/3) = 3.6329931618... - _R. J. Mathar_, Mar 08 2012
%H A168309 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (0,1).
%F A168309 a(n) = (1 - 7*(-1)^n)/2.
%F A168309 a(n) = -a(n-1) + 1 for n > 1; a(1) = 4.
%F A168309 a(n) = a(n-2) for n > 2; a(1) = 4, a(2) = -3.
%F A168309 G.f.: x*(4 - 3*x)/((1-x)*(1+x)).
%F A168309 E.g.f.: (1/2)*(-1 + exp(x))*(7 + exp(x))*exp(-x). - _G. C. Greubel_, Jul 17 2016
%t A168309 LinearRecurrence[{0,1},{4, -3}, 50] (* or *) Table[(1 - 7*(-1)^n)/2,{n,0,25}] (* _G. C. Greubel_, Jul 17 2016 *)
%t A168309 PadRight[{},120,{4,-3}] (* _Harvey P. Dale_, Oct 20 2018 *)
%o A168309 (Magma) &cat[ [4, -3]: n in [1..42] ];
%o A168309 [ n eq 1 select 4 else -Self(n-1)+1: n in [1..84] ];
%Y A168309 Cf. A010709 (all 4's sequence), A000012 (all 1's sequence), A010727 (all 7's sequence), A168230, A005009 (7*2^n), A000079 (powers of 2).
%K A168309 sign,easy
%O A168309 1,1
%A A168309 _Klaus Brockhaus_, Nov 22 2009