A168330 - OEIS

%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