OFFSET
0,1
COMMENTS
Binomial transform of (1, 1, 1, 0, 1, 0, 1, 0, 1, ...). - Gary W. Adamson, Jul 20 2007
Binomial transform of a(n) starts: 2, 6, 17, 47, 129, 355, 985, 2763, 7841, 22499, 65193, 190459, ... - Wesley Ivan Hurt, Oct 28 2014
REFERENCES
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 0..2000
Simon Plouffe, Approximations de séries génératrices et quelques conjectures, Dissertation, Université du Québec à Montréal, 1992; arXiv:0911.4975 [math.NT], 2009.
Simon Plouffe, 1031 Generating Functions, Appendix to Thesis, Montreal, 1992; arXiv:0911.4975 [math.NT], 2009.
INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 921
Index entries for linear recurrences with constant coefficients, signature (4,-5,2).
FORMULA
G.f.: (2-4*x+x^2)/((1-2*x)*(1-x)^2). - Simon Plouffe
E.g.f.: exp(x)*(exp(x)+1+x) = U(0) where U(k) = 1 + x/(2^k - 2^k/(x + 1 - x^2*2^(k+1)/(x*2^(k+1) + (k+1)/U(k+1) )));(continued fraction, 3rd kind, 4-step ). - Sergei N. Gladkovskii, Dec 01 2012
MAPLE
A005126:=-(2-4*z+z**2)/(2*z-1)/(z-1)**2; # Conjectured by Simon Plouffe in his 1992 dissertation
g:=z/(1-2*z): gser:=series(g, z=0, 43): seq(coeff(gser, z, n)+n, n=1..34); # Zerinvary Lajos, Jan 11 2009
MATHEMATICA
s=2; lst={s}; Do[s+=(s-n); AppendTo[lst, Abs[s]], {n, 0, 5!}]; lst (* Vladimir Joseph Stephan Orlovsky, Oct 10 2008 *)
Table[2^n + n + 1, {n, 0, 30}] (* Wesley Ivan Hurt, Oct 28 2014 *)
LinearRecurrence[{4, -5, 2}, {2, 4, 7}, 40] (* Harvey P. Dale, Aug 18 2016 *)
PROG
(Magma) [2^n+n+1: n in [0..40]]; // Vincenzo Librandi, Oct 22 2011
(PARI) a(n)=2^n+n+1 \\ Charles R Greathouse IV, Sep 24 2015
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
EXTENSIONS
More terms from N. J. A. Sloane, Sep 28 2007
STATUS
approved