A003479 - OEIS

A003479

Expansion of 1/((1-x)*(1-x-2*x^3)).
(Formerly M0781)

1, 2, 3, 6, 11, 18, 31, 54, 91, 154, 263, 446, 755, 1282, 2175, 3686, 6251, 10602, 17975, 30478, 51683, 87634, 148591, 251958, 427227, 724410, 1228327, 2082782, 3531603, 5988258, 10153823, 17217030, 29193547, 49501194, 83935255, 142322350

(list; graph; refs; listen; history; text; internal format)

OFFSET

0,2

REFERENCES

D. E. Daykin and S. J. Tucker, Introduction to Dragon Curves. Unpublished, 1976. See links in A003229 for an earlier version.

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

D. E. Daykin, Letter to N. J. A. Sloane, Mar 1974.

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.

Index entries for linear recurrences with constant coefficients, signature (2,-1,2,-2).

FORMULA

A003476(n+1) + A077949(n)/2 - 1/2. - Ralf Stephan, Sep 25 2004

a(n+1) - a(n) = A077949(n+1). - R. J. Mathar, Mar 22 2011

MAPLE

A003479:=1/(z-1)/(-1+z+2*z**3); # Simon Plouffe in his 1992 dissertation

MATHEMATICA

CoefficientList[Series[1/((1-x)*(1-x-2*x^3)), {x, 0, 40}], x] (* Vincenzo Librandi, Jun 12 2012 *)

PROG

(PARI) a(n)=([0, 1, 0, 0; 0, 0, 1, 0; 0, 0, 0, 1; -2, 2, -1, 2]^n*[1; 2; 3; 6])[1, 1] \\ Charles R Greathouse IV, Jun 23 2020

CROSSREFS