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 A141725 a(n) = 4^(n+1) - 3. 12
 1, 13, 61, 253, 1021, 4093, 16381, 65533, 262141, 1048573, 4194301, 16777213, 67108861, 268435453, 1073741821, 4294967293, 17179869181, 68719476733, 274877906941, 1099511627773, 4398046511101, 17592186044413, 70368744177661 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS Inverse binomial transform yields A003946 with A003946(1)=4 deleted. - R. J. Mathar, Sep 13 2008 Starting with n=1, binary numbers of the form 1X01 where X is an odd number of 1's. - Brad Clardy, Mar 22 2011 Column 4 of A193871. - Omar E. Pol, Aug 22 2011 LINKS Vincenzo Librandi, Table of n, a(n) for n = 0..1000 Index entries for linear recurrences with constant coefficients, signature (5, -4). FORMULA a(n) = 10*A001045(2*n) + A001045(2*n+1). a(n) = 4*a(n-1) + 9 for n>0, a(0)=1. a(n) = A036563(2*n+2). G.f.: (1 + 8*x)/((1 - x)*(1 - 4*x)). - R. J. Mathar, Sep 13 2008 a(n) = 4^n - 3, with offset 1. - Omar E. Pol, Aug 22 2011 a(n) = 5*a(n-1) - 4*a(n-2) for n>1, a(0)=1, a(1)=13. - Harvey P. Dale, Sep 25 2011 MAPLE a:= n-> 4^(n+1)-3: seq(a(n), n=0..25); # Muniru A Asiru, Feb 20 2018 MATHEMATICA 4^(Range[2, 25]-1)-3 (* or *) LinearRecurrence[{5, -4}, {1, 13}, 25] (* or *) NestList[4#+9&, 1, 25] (* Harvey P. Dale, Sep 25 2011 *) PROG (MAGMA) [4^(n+1)-3: n in [0..30]]; // Vincenzo Librandi, Aug 08 2011 (PARI) a(n)=4^(n+1)-3 \\ Charles R Greathouse IV, Oct 07 2015 (GAP) List([0..25], n -> 4^(n+1)-3); # Muniru A Asiru, Feb 20 2018 CROSSREFS Cf. A001045, A036563. Sequence in context: A252970 A047673 A231800 * A279762 A147185 A122885 Adjacent sequences:  A141722 A141723 A141724 * A141726 A141727 A141728 KEYWORD nonn,easy AUTHOR Paul Curtz, Sep 13 2008 EXTENSIONS Edited by N. J. A. Sloane, Sep 13 2008 More terms from R. J. Mathar, Sep 13 2008 STATUS approved

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Last modified July 4 16:46 EDT 2022. Contains 355081 sequences. (Running on oeis4.)