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A163403
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a(n) = 2*a(n-2) for n > 2; a(1) = 1, a(2) = 2.
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7
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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
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OFFSET
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1,2
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COMMENTS
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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
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LINKS
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Vincenzo Librandi, Table of n, a(n) for n = 1..1000
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FORMULA
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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
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EXAMPLE
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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 + ...
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PROG
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(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(); [next(a) for i in range(40)] # Peter Luschny, Jul 11 2013
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CROSSREFS
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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 A306663 A222955
Adjacent sequences: A163400 A163401 A163402 * A163404 A163405 A163406
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KEYWORD
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nonn
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AUTHOR
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Klaus Brockhaus, Jul 26 2009
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STATUS
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approved
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