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A003478 Expansion of 1/(1-2x)(1-x-2x^3 ).
(Formerly M2662)
1
1, 3, 7, 17, 39, 85, 183, 389, 815, 1693, 3495, 7173, 14655, 29837, 60567, 122645, 247855, 500061, 1007495, 2027493, 4076191, 8188333, 16437623, 32978613, 66132495, 132562173, 265628263, 532110981, 1065670783, 2133798221, 4271762007, 8550587221, 17113150959 (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 Unpublished, 1976.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.

Simon Plouffe, 1031 Generating Functions and Conjectures, Université du Québec à Montréal, 1992.

Index entries for linear recurrences with constant coefficients, signature (3,-2,2,-4)

FORMULA

2^n - 3 * A003476(n+1) + A052537(n). - Ralf Stephan, Sep 25 2004

MAPLE

A003478:=1/(2*z-1)/(-1+z+2*z**3); [Conjectured by Simon Plouffe in his 1992 dissertation.]

MATHEMATICA

CoefficientList[Series[1/((1-2x)(1-x-2x^3)), {x, 0, 50}], x]  (* Harvey P. Dale, Mar 14 2011 *)

PROG

(PARI) Vec(1/(1-2*x)*(1-x-2*x^3)+O(x^99)) \\ Charles R Greathouse IV, Sep 26 2012

CROSSREFS

Sequence in context: A176502 A319003 A141199 * A119587 A127984 A157029

Adjacent sequences:  A003475 A003476 A003477 * A003479 A003480 A003481

KEYWORD

nonn,easy

AUTHOR

N. J. A. Sloane.

EXTENSIONS

More terms from Harvey P. Dale, Mar 14 2011.

STATUS

approved

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Last modified May 26 17:16 EDT 2020. Contains 334630 sequences. (Running on oeis4.)