A168090 a(n) = (1 - (n mod 3) mod 2)*2^(floor(n/3) + (n mod 3)/2 ).

1, 0, 2, 2, 0, 4, 4, 0, 8, 8, 0, 16, 16, 0, 32, 32, 0, 64, 64, 0, 128, 128, 0, 256, 256, 0, 512, 512, 0, 1024, 1024, 0, 2048, 2048, 0, 4096, 4096, 0, 8192, 8192, 0, 16384, 16384, 0, 32768, 32768, 0, 65536, 65536, 0, 131072, 131072, 0, 262144, 262144, 0, 524288

Offset

0,3

Comments

Equals the INVERT transform of (1, -1, 3, -3, 3, -3, ...) (with infinitely repeating 3, -3).

References

K. Rosen, Discrete Mathematics and Its Applications, McGraw-Hill Science/Engineering/Math; 6 edition (Jul 26 2006), Section 4.3 Exercise 6b

Links

G. C. Greubel, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (0,0,2).

Formula

From Colin Barker, Aug 21 2016: (Start)

a(n) = 2*a(n-3) for n>2.

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

(End)

Mathematica

f[n_] := 2^(Floor[n/3] + Mod[n, 3]/2) Mod[1 - Mod[n, 3], 2]; Array[f, 60, 0] (* Robert G. Wilson v, Aug 03 2010 *)

Prog

(PARI) a(n)=[1, 0, 2][n%3+1]<<(n\3) \\ Charles R Greathouse IV, Jul 12 2016
(PARI) Vec((1+2*x^2)/(1-2*x^3) + O(x^50)) \\ Colin Barker, Aug 21 2016

Crossrefs

Sequence in context: A181615 A141333 A262967 * A078029 A078030 A262056

Adjacent sequences: A168087 A168088 A168089 * A168091 A168092 A168093

Keyword

easy,nonn

Author

_Frank Cheng_, Nov 18 2009

Extensions

More terms from Robert G. Wilson v, Aug 03 2010

Status

approved