A161204 a(0)=2. a(n+1) = 2*a(n) + period 4: repeat -5,1,3,1.

2, -1, -1, 1, 3, 1, 3, 9, 19, 33, 67, 137, 275, 545, 1091, 2185, 4371, 8737, 17475, 34953, 69907, 139809, 279619, 559241, 1118483, 2236961, 4473923, 8947849, 17895699, 35791393, 71582787, 143165577, 286331155, 572662305, 1145324611, 2290649225, 4581298451, 9162596897

Offset: 0

Author

Paul Curtz, Jan 20 2011

Keywords

• sign
• easy

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (1,1,1,2).

Programs

Magma

I:=[2, -1, -1, 1]; [n le 4 select I[n] else Self(n-1)+Self(n-2)+Self(n-3)+2*Self(n-4): n in [1..40]]; // Vincenzo Librandi, Jun 17 2012

Maple

A000034 := proc(n) if type(n,'even') then 1 ; else 2 ; end if; end proc:
A161204 := proc(n) 4*(-1)^floor((n+1)/2)*A000034(n+1)/5+2^n/15+(-1)^n/3 ; end proc: # R. J. Mathar, Jan 26 2011

Mathematica

CoefficientList[Series[(-2+3*x-x^3+2*x^2)/((2*x-1)*(1+x)*(1+x^2)),{x,0,40}],x] (* Vincenzo Librandi, Jun 17 2012 *)
LinearRecurrence[{1,1,1,2},{2,-1,-1,1},40] (* Harvey P. Dale, Dec 01 2019 *)

Formula

First differences of A180343(n).

G.f.: ( -2 + 3*x - x^3 + 2*x^2 ) / ( (2*x-1)*(1+x)*(1+x^2) ). - R. J. Mathar, Jan 26 2011

a(n) = 4*(-1)^floor((n+1)/2)*A000034(n+1)/5 + 2^n/15 + (-1)^n/3. - R. J. Mathar, Jan 26 2011

a(n) = a(n-4) + 2^(n-4).

a(n) = a(n-2) + (-3,2,4,0,0,8,16,24,=sixth differences of A007910(n-1) = 0,0,1,2,3,6,13 or fifth differences of A007909(n); also -3,2,4,8*A007910(n-1)).

a(n) = a(n-1) + a(n-2) + a(n-3) + 2*a(n-4). - Vincenzo Librandi, Jun 17 2012