A168330 Period 2: repeat [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, 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, 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

Offset: 1

Author

Klaus Brockhaus, Nov 23 2009

Keywords

• sign
• easy

Comments

Interleaving of A010701 and -A007395.

Binomial transform of 3 followed by a signed version of A020714.

Inverse binomial transform of 3 followed by A000079.

A084964 without first two terms gives partial sums.

Links

• Index entries for linear recurrences with constant coefficients, signature (0,1).

Crossrefs

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).

Programs

Magma

&cat[[3,-2]: n in [1..42]];

Magma

[n eq 1 select 3 else -Self(n-1)+1:n in [1..84]];

Magma

[(-5*(-1)^n+1)/2: n in [1..100]]; // Vincenzo Librandi, Jul 19 2016

Mathematica

LinearRecurrence[{0, 1}, {3, -2}, 25] (* G. C. Greubel, Jul 18 2016 *)
PadRight[{},120,{3,-2}] (* Harvey P. Dale, Oct 05 2016 *)

PARI

a(n)=3-n%2*5 \\ Charles R Greathouse IV, Jul 13 2016

Formula

a(n) = (-5*(-1)^n + 1)/2.

a(n+1) - a(n) = 5*(-1)^n.

a(n) = -a(n-1) + 1 for n > 1; a(1) = 3.

a(n) = a(n-2) for n > 2; a(1) = 3, a(2) = -2.

G.f.: x*(3 - 2*x)/((1-x)*(1+x)).

a(n) = A049071(n). - R. J. Mathar, Nov 25 2009

E.g.f.: (1/2)*(1 - exp(-x))*(5 + exp(x)). - G. C. Greubel, Jul 18 2016