A003479 Expansion of 1/((1-x)*(1-x-2*x^3)).

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

Offset: 0

Author

N. J. A. Sloane

Keywords

• easy
• nonn

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 Unpublished, 1976.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).

Crossrefs

Cf. A003229.

Programs

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 *)

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

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

Extensions

More terms from Antonio G. Astudillo (afg_astudillo(AT)lycos.com), Mar 29 2003