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A068922 Number of ways to tile a 3 X 2n room with 1 X 2 Tatami mats. At most 3 Tatami mats may meet at a point. 8
3, 4, 6, 10, 16, 26, 42, 68, 110, 178, 288, 466, 754, 1220, 1974, 3194, 5168, 8362, 13530, 21892, 35422, 57314, 92736, 150050, 242786, 392836, 635622, 1028458, 1664080, 2692538, 4356618, 7049156, 11405774, 18454930, 29860704, 48315634, 78176338, 126491972 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

LINKS

Colin Barker, Table of n, a(n) for n = 1..1000

R. J. Mathar, Paving rectangular regions with rectangular tiles,...., arXiv:1311.6135 [math.CO], 2013, Table 2.

F. Ruskey and J. Woodcock, Counting Fixed-Height Tatami Tilings, Electronic Journal of Combinatorics, Paper R126 (2009) 20 pages.

Index entries for linear recurrences with constant coefficients, signature (1,1).

FORMULA

For n >= 2, a(n) = 2*F(n+1), where F(n)=A000045(n) is the n-th Fibonacci number.

G.f.: x*(x^2-x-3) / (x^2+x-1). - Maksym Voznyy (voznyy(AT)mail.ru), Aug 11 2009; checked and corrected by R. J. Mathar, Sep 16 2009

From Colin Barker, Jan 29 2017: (Start)

a(n) = (2^(-n)*(-(1-sqrt(5))^(1+n) + (1+sqrt(5))^(1+n))) / sqrt(5) for n>1.

a(n) = a(n-1) + a(n-2) for n>3.

(End)

PROG

(PARI) Vec(x*(3+x-x^2) / (1-x-x^2) + O(x^50)) \\ Colin Barker, Jan 29 2017

CROSSREFS

Cf. A068928 for incongruent tilings, A068920 for more info. First column of A272472.

Essentially the same as A006355.

Sequence in context: A139463 A287067 A214289 * A032408 A018908 A052548

Adjacent sequences:  A068919 A068920 A068921 * A068923 A068924 A068925

KEYWORD

easy,nonn

AUTHOR

Dean Hickerson, Mar 11 2002

STATUS

approved

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Last modified September 23 15:54 EDT 2017. Contains 292361 sequences.