A168309 Period 2: repeat 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, 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, 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

Offset: 1

Author

Klaus Brockhaus, Nov 22 2009

Keywords

• sign
• easy

Comments

Interleaving of A010709 and -3*A000012.

Binomial transform of 4 followed by a signed version of A005009.

Inverse binomial transform of 4 followed by A000079.

a(n+1) - a(n) = 7*(-1)^n.

A168230 without initial term 0 gives partial sums.

Nonsimple continued fraction expansion of 2+2*sqrt(2/3) = 3.6329931618... - R. J. Mathar, Mar 08 2012

Links

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

Crossrefs

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).

Programs

Magma

&cat[ [4, -3]: n in [1..42] ];
[ n eq 1 select 4 else -Self(n-1)+1: n in [1..84] ];

Mathematica

LinearRecurrence[{0,1},{4, -3}, 50] (* or *) Table[(1 - 7*(-1)^n)/2,{n,0,25}] (* G. C. Greubel, Jul 17 2016 *)
PadRight[{},120,{4,-3}] (* Harvey P. Dale, Oct 20 2018 *)

Formula

a(n) = (1 - 7*(-1)^n)/2.

a(n) = -a(n-1) + 1 for n > 1; a(1) = 4.

a(n) = a(n-2) for n > 2; a(1) = 4, a(2) = -3.

G.f.: x*(4 - 3*x)/((1-x)*(1+x)).

E.g.f.: (1/2)*(-1 + exp(x))*(7 + exp(x))*exp(-x). - G. C. Greubel, Jul 17 2016