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A077958 Expansion of 1/(1-2*x^3). 4
1, 0, 0, 2, 0, 0, 4, 0, 0, 8, 0, 0, 16, 0, 0, 32, 0, 0, 64, 0, 0, 128, 0, 0, 256, 0, 0, 512, 0, 0, 1024, 0, 0, 2048, 0, 0, 4096, 0, 0, 8192, 0, 0, 16384, 0, 0, 32768, 0, 0, 65536, 0, 0, 131072, 0, 0, 262144, 0, 0, 524288, 0, 0, 1048576, 0, 0, 2097152, 0, 0, 4194304, 0, 0, 8388608, 0 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,4

COMMENTS

a(n) is the number of L-tromino tilings of the n X 2 rectangle (see Exercise 2 in Grinberg). - Stefano Spezia, Nov 26 2019

LINKS

G. C. Greubel, Table of n, a(n) for n = 0..1002

Darij Grinberg, Math 222: Enumerative Combinatorics, Fall 2019: Homework 1, Drexel University, Department of Mathematics, 2019.

Index entries for linear recurrences with constant coefficients, signature (0,0,2).

FORMULA

G.f.: A(x) = x/(x-1)*G(0); G(k) = 1 - 1/(x - 2*x^5/(2*x^4 - 1/G(k+1))); (continued fraction, 3-step). - Sergei N. Gladkovskii, Nov 25 2012

From Stefano Spezia, Nov 26 2019: (Start)

a(n) = 2^(n/3) if 3 divides n, otherwise a(n) = 0 (see Exercise 2 in Grinberg).

E.g.f.: (1/3)*(exp(-(-2)^(1/3)*x) + exp(2^(1/3)*x) + exp((-1)^(2/3)*2^(1/3)*x)).

(End)

MATHEMATICA

CoefficientList[Series[1/(1-2*x^3), {x, 0, 80}], x] (* or *) LinearRecurrence[{0, 0, 2}, {1, 0, 0}, 80] (* Vladimir Joseph Stephan Orlovsky, Jan 30 2012 *)

Riffle[Riffle[2^Range[0, 30], 0], 0, {3, -1, 3}] (* Harvey P. Dale, Dec 18 2012 *)

PROG

(PARI) Vec(1/(1-2*x^3)+O(x^80)) \\ Charles R Greathouse IV, Sep 27 2012

(MAGMA) R<x>:=PowerSeriesRing(Integers(), 80); Coefficients(R!( 1/(1-2*x^3) )); // G. C. Greubel, Jun 23 2019

(Sage) (1/(1-2*x^3)).series(x, 80).coefficients(x, sparse=False) # G. C. Greubel, Jun 23 2019

CROSSREFS

Cf. A006801, A162673, A163433, A329185.

Sequence in context: A319935 A136337 A028601 * A077959 A022002 A084658

Adjacent sequences:  A077955 A077956 A077957 * A077959 A077960 A077961

KEYWORD

nonn,easy

AUTHOR

N. J. A. Sloane, Nov 17 2002

STATUS

approved

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Last modified May 6 02:09 EDT 2021. Contains 343579 sequences. (Running on oeis4.)