A005262 a(n) = floor((7*2^(n+1)-9*n-10)/3). (Formerly M2793)

1, 3, 9, 25, 59, 131, 277, 573, 1167, 2359, 4745, 9521, 19075, 38187, 76413, 152869, 305783, 611615, 1223281, 2446617, 4893291, 9786643, 19573349, 39146765, 78293599, 156587271, 313174617, 626349313, 1252698707, 2505397499, 5010795085, 10021590261

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).

Index entries for sequences related to Towers of Hanoi

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

Sequence in context: A293852 A005209 A112522 * A101357 A004255 A065971

Adjacent sequences: A005259 A005260 A005261 * A005263 A005264 A005265

Keyword

nonn,easy

Author

N. J. A. Sloane

Extensions

Definition corrected by Colin Barker, Jan 12 2012

Status

approved