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A163403 a(n) = 2*a(n-2) for n > 2; a(1) = 1, a(2) = 2. 6
1, 2, 2, 4, 4, 8, 8, 16, 16, 32, 32, 64, 64, 128, 128, 256, 256, 512, 512, 1024, 1024, 2048, 2048, 4096, 4096, 8192, 8192, 16384, 16384, 32768, 32768, 65536, 65536, 131072, 131072, 262144, 262144, 524288, 524288, 1048576, 1048576, 2097152, 2097152 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Equals A016116 without initial 1. Unsigned version of A152166.

Partial sums are in A136252. a(n) = A051032(n)-1.

Binomial transform is A078057, second binomial transform is A007070, third binomial transform is A102285, fourth binomial transform is A163350, fifth binomial transform is A163346.

a(n+1) is the number of palindromic words of length n using a two-letter alphabet. - Michael Somos, Mar 20 2011

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 1..1000

FORMULA

a(n) = 2^(1/4*(2*n-1+(-1)^n)).

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

G.f.: x / (1 - 2*x / (1 + x / (1 + x))) = x * (1 + 2*x / (1 - x / (1 - x / (1 + 2*x)))). - Michael Somos, Jan 03 2013

From R. J. Mathar, Aug 06 2009: (Start)

a(n) = A131572(n).

a(n) = A060546(n-1), n > 1. (End)

a(n+3) = a(n+2)*a(n+1)/a(n). - Reinhard Zumkeller, Mar 04 2011

a(n) = |A009116(n-1)| + |A009545(n-1)|. - Bruno Berselli, May 30 2011

EXAMPLE

x + 2*x^2 + 2*x^3 + 4*x^4 + 4*x^5 + 8*x^6 + 8*x^7 + 16*x^8 + 16*x^9 + 32*x^10 + ...

PROG

(MAGMA) [ n le 2 select n else 2*Self(n-2): n in [1..43] ];

(PARI) {a(n) = if( n<1, 0, 2^(n\2))} /* Michael Somos, Mar 20 2011 */

(Sage)

def A163403():

    x, y = 1, 1

    while true:

        yield x

        x, y = x + y, x - y

a = A163403(); [a.next() for i in range(40)]  # Peter Luschny, Jul 11 2013

CROSSREFS

Cf. A000079 (powers of 2), A016116 (powers of 2 doubled up), A152166, A136252, A051032, A078057, A007070, A102285, A163350, A163346.

Sequence in context: A320770 A016116 A060546 * A231208 A222955 A217208

Adjacent sequences:  A163400 A163401 A163402 * A163404 A163405 A163406

KEYWORD

nonn

AUTHOR

Klaus Brockhaus, Jul 26 2009

STATUS

approved

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Last modified February 22 15:52 EST 2019. Contains 320399 sequences. (Running on oeis4.)