A168361 Period 2: repeat 2, -1.

2, -1, 2, -1, 2, -1, 2, -1, 2, -1, 2, -1, 2, -1, 2, -1, 2, -1, 2, -1, 2, -1, 2, -1, 2, -1, 2, -1, 2, -1, 2, -1, 2, -1, 2, -1, 2, -1, 2, -1, 2, -1, 2, -1, 2, -1, 2, -1, 2, -1, 2, -1, 2, -1, 2, -1, 2, -1, 2, -1, 2, -1, 2, -1, 2, -1, 2, -1, 2, -1, 2, -1, 2, -1, 2, -1, 2, -1, 2, -1, 2, -1, 2, -1

Offset: 1

Author

Klaus Brockhaus, Nov 23 2009

Keywords

• sign
• easy

Comments

Interleaving of A007395 and -A000012.

Binomial transform of 2 followed by a signed version of A007283; also binomial transform of a signed version of A042950.

Second binomial transform of a signed version of A007051 without initial term 1.

Inverse binomial transform of 2 followed by A000079.

A028242 without first two terms gives partial sums.

Links

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

Crossrefs

Cf. A168330 (repeat 3, -2), A007395 (all 2's sequence), A000012 (all 1's sequence), (A007283 3*2^n), A042950, A007051 ((3^n+1)/2), A000079 (powers of 2), A028242 (follow n+1 by n).

Programs

Magma

&cat[ [2, -1]: n in [1..42] ];
[ n eq 1 select 2 else -Self(n-1)+1: n in [1..84] ];

Magma

&cat[[2,-1]^^40]; // Vincenzo Librandi, Jul 20 2016

Mathematica

PadRight[{},120,{2,-1}] (* Harvey P. Dale, Jan 04 2015 *)
Table[(1 - 3 (-1)^n)/2, {n, 120}] (* or *)
Rest@ CoefficientList[Series[x (2 - x)/((1 - x) (1 + x)), {x, 0, 120}], x] (* Michael De Vlieger, Jul 19 2016 *)

PARI

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

Formula

a(n) = (1 - 3*(-1)^n)/2.

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

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

a(n+1) - a(n) = 3*(-1)^n.

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

E.g.f.: (1/2)*(-1 + exp(x))*(3 + exp(x))*exp(-x). - G. C. Greubel, Jul 19 2016

Extensions

G.f. adapted to the offset by Bruno Berselli, Apr 01 2011