OFFSET
0,2
COMMENTS
Arises from Tower of Hanoi problem.
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..1000
Andy Liu and Steve Newman, Problem 1169, Crux Mathematicorum, 13 (No. 10, 1987), 328-332. Also annotated scanned copy.
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
L. J. Upton, Letter, Jan 1991
Index entries for linear recurrences with constant coefficients, signature (3,-1,-3,2).
FORMULA
G.f.: (1+x^2+4*x^3)/((1+x)*(1-2*x)*(1-x)^2) = (1+x^2+4*x^3)/(1-3*x+x^2+3*x^3-2*x^4). - Simon Plouffe (see MAPLE line) and Bruno Berselli, Jan 12 2012
a(n) = (28*2^n-18*n-(-1)^n-21)/6 = (7*2^(n+1)-9*n-10)/3-((-1)^n+1)/6. - Bruno Berselli, Jan 12 2012
MAPLE
A005262:=-(1+z**2+4*z**3)/((z+1)*(2*z-1)*(z-1)**2); # [Simon Plouffe in his 1992 dissertation.]
MATHEMATICA
CoefficientList[Series[-(1+x^2+4*x^3)/((x+1)*(2*x-1)*(x-1)^2), {x, 0, 30}], x] (* Vincenzo Librandi, Apr 16 2012 *)
LinearRecurrence[{3, -1, -3, 2}, {1, 3, 9, 25}, 40] (* Harvey P. Dale, Jan 01 2015 *)
PROG
(Magma)[Floor((7*2^(n+1)-9*n-10)/3): n in [0..30]]; // Vincenzo Librandi, Apr 16 2012
(PARI) a(n)=(14<<n-9*n-10)\3 \\ Charles R Greathouse IV, Jun 28 2017
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
EXTENSIONS
Definition corrected by Colin Barker, Jan 12 2012
STATUS
approved