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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.)