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A135520 a(n) = 4*a(n-2). 8
2, 1, 8, 4, 32, 16, 128, 64, 512, 256, 2048, 1024, 8192, 4096, 32768, 16384, 131072, 65536, 524288, 262144, 2097152, 1048576, 8388608, 4194304, 33554432, 16777216, 134217728, 67108864, 536870912, 268435456, 2147483648, 1073741824 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,1

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (0, 4).

FORMULA

From R. J. Mathar, corrected Apr 14 2008: (Start)

O.g.f.: (5/(1-2*x) + 3/(1+2*x))/4.

a(n) = (5*2^n + 3*(-2)^n)/4.

a(2*n)=2*A000302(n). a(2*n+1)=A000302(n). (End)

a(n) = (1/4)*(5*2^n + 3*(-2)^n), with n>=0 - Paolo P. Lava, Jun 06 2008

a(n) = A000079(n) terms swapped by pairs. - Paul Curtz, Apr 26 2011

a(n) = 2^(n+(-1)^n). - Wesley Ivan Hurt, Dec 13 2013

E.g.f.: (1/4)*(5*exp(2*x) + 3*exp(-2*x)). - G. C. Greubel, Oct 17 2016

MAPLE

A135520:=n->2^(n+(-1)^n); seq(A135520(n), n=0..50); # Wesley Ivan Hurt, Dec 13 2013

MATHEMATICA

LinearRecurrence[{1, 4, -4}, {2, 1, 8}, 40] (* Harvey P. Dale, May 25 2012 *)

LinearRecurrence[{0, 4}, {2, 1}, 32] (* Ray Chandler, Aug 03 2015 *)

PROG

(PARI) a(n)=1<<(n+(-1)^n) \\ Charles R Greathouse IV, Jun 01 2011

(MAGMA) [(5/4)*2^n+(3/4)*(-2)^n: n in [0..40]]; // Vincenzo Librandi, Jun 02 2011

CROSSREFS

Cf. A097163, A097164.

Sequence in context: A223550 A178102 A245836 * A136230 A193892 A193907

Adjacent sequences:  A135517 A135518 A135519 * A135521 A135522 A135523

KEYWORD

nonn,easy

AUTHOR

Paul Curtz, Feb 19 2008

EXTENSIONS

More terms from R. J. Mathar, Feb 23 2008

STATUS

approved

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Last modified August 18 18:19 EDT 2017. Contains 290737 sequences.