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A068921 Number of ways to tile a 2 X n room with 1x2 Tatami mats. At most 3 Tatami mats may meet at a point. 9
1, 1, 2, 3, 4, 6, 9, 13, 19, 28, 41, 60, 88, 129, 189, 277, 406, 595, 872, 1278, 1873, 2745, 4023, 5896, 8641, 12664, 18560, 27201, 39865, 58425, 85626, 125491, 183916, 269542, 395033, 578949, 848491, 1243524, 1822473, 2670964, 3914488, 5736961 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

LINKS

G. C. Greubel, Table of n, a(n) for n = 0..1000

R. J. Mathar, Paving rectangular regions with rectangular tiles: Tatami and Non-Tatami Tilings, arXiv:1311.6135 [math.CO], 2013, Table 1.

Index entries for linear recurrences with constant coefficients, signature (1,0,1).

FORMULA

For n >= 3, a(n) = a(n-1) + a(n-3).

a(n) = A000930(n+1).

From Frank Ruskey, Jun 07 2009: (Start)

G.f.: (1+x^2)/(1-x-x^3).

a(n) = sum( binomial(n-2j+1,j), j=0..floor(n/2) ). (End)

G.f.: Q(0)*( 1+x^2 )/2, where Q(k) = 1 + 1/(1 - x*(4*k+1 + x^2)/( x*(4*k+3 + x^2) + 1/Q(k+1) )); (continued fraction). - Sergei N. Gladkovskii, Sep 08 2013

MATHEMATICA

LinearRecurrence[{1, 0, 1}, {1, 1, 2}, 42] (* Robert G. Wilson v, Jul 12 2014 *)

PROG

(PARI) x='x+O('x^50); Vec((1+x^2)/(1-x-x^3)) \\ G. C. Greubel, Apr 26 2017

CROSSREFS

Cf. A068927 for incongruent tilings, A068920 for more info.

Cf. A000930, A078012, first column of A272471.

Sequence in context: A247083 A159848 A017826 * A000930 A078012 A135851

Adjacent sequences:  A068918 A068919 A068920 * A068922 A068923 A068924

KEYWORD

nonn,easy

AUTHOR

Dean Hickerson, Mar 11 2002

STATUS

approved

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Last modified June 28 05:07 EDT 2017. Contains 288813 sequences.