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%I #20 Sep 08 2022 08:45:49
%S 3,-2,3,-2,3,-2,3,-2,3,-2,3,-2,3,-2,3,-2,3,-2,3,-2,3,-2,3,-2,3,-2,3,
%T -2,3,-2,3,-2,3,-2,3,-2,3,-2,3,-2,3,-2,3,-2,3,-2,3,-2,3,-2,3,-2,3,-2,
%U 3,-2,3,-2,3,-2,3,-2,3,-2,3,-2,3,-2,3,-2,3,-2,3,-2,3,-2,3,-2,3,-2,3,-2,3,-2
%N Period 2: repeat [3, -2].
%C Interleaving of A010701 and -A007395.
%C Binomial transform of 3 followed by a signed version of A020714.
%C Inverse binomial transform of 3 followed by A000079.
%C A084964 without first two terms gives partial sums.
%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (0,1).
%F a(n) = (-5*(-1)^n + 1)/2.
%F a(n+1) - a(n) = 5*(-1)^n.
%F a(n) = -a(n-1) + 1 for n > 1; a(1) = 3.
%F a(n) = a(n-2) for n > 2; a(1) = 3, a(2) = -2.
%F G.f.: x*(3 - 2*x)/((1-x)*(1+x)).
%F a(n) = A049071(n). - _R. J. Mathar_, Nov 25 2009
%F E.g.f.: (1/2)*(1 - exp(-x))*(5 + exp(x)). - _G. C. Greubel_, Jul 18 2016
%t LinearRecurrence[{0, 1}, {3, -2}, 25] (* _G. C. Greubel_, Jul 18 2016 *)
%t PadRight[{},120,{3,-2}] (* _Harvey P. Dale_, Oct 05 2016 *)
%o (Magma) &cat[[3,-2]: n in [1..42]];
%o (Magma) [n eq 1 select 3 else -Self(n-1)+1:n in [1..84]];
%o (Magma) [(-5*(-1)^n+1)/2: n in [1..100]]; // _Vincenzo Librandi_, Jul 19 2016
%o (PARI) a(n)=3-n%2*5 \\ _Charles R Greathouse IV_, Jul 13 2016
%Y Cf. A168309 (repeat 4, -3), A010701 (all 3's sequence), A007395 (all 2's sequence), A010716 (all 5's sequence), A020714 (5*2^n), A000079 (powers of 2), A084964 (follow n+2 by n).
%K sign,easy
%O 1,1
%A _Klaus Brockhaus_, Nov 23 2009
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