OFFSET
0,1
COMMENTS
From Greg Dresden, May 08 2023: (Start)
For n >= 3, 2*a(n) is the number of ways to tile this figure of length n-1 with two colors of squares and one color of domino. For n=8, we have here the figure of length n-1=7, and it has 2*a(8) = 2728 different tilings.
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(End)
LINKS
Reinhard Zumkeller, Table of n, a(n) for n = 0..1000
José L. Ramírez, Gustavo N. Rubiano, and Rodrigo de Castro, A Generalization of the Fibonacci Word Fractal and the Fibonacci Snowflake, arXiv preprint arXiv:1212.1368 [cs.DM], 2012-2014.
Index entries for linear recurrences with constant coefficients, signature (2,1).
FORMULA
G.f.: -(13*x-4) / (x^2+2*x-1). - Colin Barker, Jul 10 2015
a(n) is the numerator of the continued fraction [4, 2, ..., 2, 4] with n-3 2's in the middle. For denominators, see A048654. - Greg Dresden and Tongjia Rao, Sep 02 2021
MATHEMATICA
LinearRecurrence[{2, 1}, {-4, 5}, 50] (* Paolo Xausa, Sep 02 2024 *)
PROG
(Haskell)
a221174 n = a221174_list !! n
a221174_list = -4 : 5 : zipWith (+)
(map (* 2) $ tail a221174_list) a221174_list
-- Reinhard Zumkeller, Jan 04 2013
(PARI) Vec(-(13*x-4)/(x^2+2*x-1) + O(x^50)) \\ Colin Barker, Jul 10 2015
CROSSREFS
KEYWORD
sign,easy
AUTHOR
N. J. A. Sloane, Jan 04 2013
STATUS
approved