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 A168607 a(n) = 3^n + 2. 13
 3, 5, 11, 29, 83, 245, 731, 2189, 6563, 19685, 59051, 177149, 531443, 1594325, 4782971, 14348909, 43046723, 129140165, 387420491, 1162261469, 3486784403, 10460353205, 31381059611, 94143178829, 282429536483, 847288609445 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,1 COMMENTS Second bisection is A134752. It appears that if s(n) is a first order rational sequence of the form s(1)=5, s(n)= (2*s(n-1)+1)/(s(n-1)+2),n>1, then s(n)= a(n)/(a(n)-4), n>1. - Gary Detlefs, Nov 16 2010 Mahler exhibits this sequence with n>=1 as a proof that there exists an infinite number of x coprime to 3, such that x belongs to A125293 and x^2 belongs to A005836. - Michel Marcus, Nov 12 2012 LINKS Vincenzo Librandi, Table of n, a(n) for n = 0..1000 Gennady Eremin, Arithmetization of well-formed parenthesis strings. Motzkin Numbers of the Second Kind, arXiv:2012.12675 [math.CO], 2020. Kurt Mahler, The representation of squares to the base 3, Acta Arith. Vol. 53, Issue 1 (1989), p. 99-106. Index entries for linear recurrences with constant coefficients, signature (4,-3). FORMULA a(n) = 3*a(n-1)-4, a(0) = 3. a(n+1)-a(n) = A008776(n). a(n+2)-a(n) = A005051(n). a(n) = A034472(n)+1 = A000244(n)+2 = A024023(n)+3 = A168609(n)-2 = A168610(n)-3. G.f.: (3-7*x)/((1-x)*(1-3*x)). a(n) = 4*a(n-1) - 3*a(n-2), a(0)=3, a(1)=5. - Vincenzo Librandi, Feb 06 2013 MAPLE A168607:=n->3^n + 2; seq(A168607(n), n=0..30); # Wesley Ivan Hurt, Mar 21 2014 MATHEMATICA CoefficientList[Series[(3 - 7 x)/((1-x) (1-3 x)), {x, 0, 30}], x] (* Vincenzo Librandi, Feb 06 2013 *) NestList[3 # - 4 & , 3, 25] (* Bruno Berselli, Feb 06 2013 *) PROG (MAGMA) [3^n+2: n in [0..30]]; (PARI) a(n)=3^n+2 \\ Charles R Greathouse IV, Oct 07 2015 CROSSREFS Cf. A008776 (2*3^n), A005051 (8*3^n), A034472 (3^n+1), A000244 (powers of 3), A024023 (3^n-1), A168609 (3^n+4), (A168610 3^n+5), A134752 (3^(2*n-1)+2). Sequence in context: A279674 A194563 A080443 * A057735 A095302 A335367 Adjacent sequences:  A168604 A168605 A168606 * A168608 A168609 A168610 KEYWORD nonn,easy AUTHOR Vincenzo Librandi, Dec 01 2009 EXTENSIONS Edited by Klaus Brockhaus, Apr 13 2010 Further edited by N. J. A. Sloane, Aug 10 2010 STATUS approved

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Last modified August 10 03:28 EDT 2022. Contains 356029 sequences. (Running on oeis4.)