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
KEYWORD
nonn,easy
AUTHOR
N. J. A. Sloane, Nov 17 2002
STATUS
approved