The On-Line Encyclopedia of Integer Sequences (OEIS)

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A068923

Number of ways to tile a 4 X n room with 1x2 Tatami mats. At most 3 Tatami mats may meet at a point.
(history; published version)

#10 by R. J. Mathar at Thu Oct 17 11:44:28 EDT 2019

STATUS

editing

approved

#9 by R. J. Mathar at Thu Oct 17 11:44:24 EDT 2019

LINKS

<a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (0,0,1,0,1).

STATUS

approved

editing

#8 by R. J. Mathar at Sun May 01 12:51:19 EDT 2016

STATUS

editing

approved

#7 by R. J. Mathar at Sun May 01 12:51:12 EDT 2016

CROSSREFS

Cf. A068929 for incongruent tilings, A068920 for more info. First column of A272473.

EXTENSIONS

G.f. proposed by Maksym Voznyy checked and corrected by _R. J. Mathar, _, Sep 16 2009.

STATUS

approved

editing

#6 by N. J. A. Sloane at Tue Jun 24 01:08:23 EDT 2014

AUTHOR

_Dean Hickerson (dean.hickerson(AT)yahoo.com), _, Mar 11 2002

Discussion

Tue Jun 24

01:08

OEIS Server: https://oeis.org/edit/global/2238

#5 by R. J. Mathar at Tue Nov 26 14:37:39 EST 2013

STATUS

editing

approved

#4 by R. J. Mathar at Tue Nov 26 14:37:31 EST 2013

LINKS

R. J. Mathar, <a href="http://arxiv.org/abs/1311.6135">Paving rectangular regions with rectangular tiles,....</a>, arXiv:1311.6135 [math.CO], Table 3.

STATUS

approved

editing

#3 by N. J. A. Sloane at Tue Jun 01 03:00:00 EDT 2010

FORMULA

G.f.: x*(x+1)*(2*x^6+x^5+x^4-x^2-3*x-1)/(-1+x^5+x^3) [From Maksym Voznyy (voznyy(AT)mail.ru), Jul 28 2009]

KEYWORD

easy,nonn,new

EXTENSIONS

G.f. proposed by Maksym Voznyy checked and corrected by R. J. Mathar, Sep 16 2009.

#2 by N. J. A. Sloane at Fri Jan 09 03:00:00 EST 2009

KEYWORD

easy,nonn,new

AUTHOR

Dean Hickerson (dean.hickerson(AT)math.ucdavisyahoo.educom), Mar 11 2002

#1 by N. J. A. Sloane at Fri May 16 03:00:00 EDT 2003

NAME

Number of ways to tile a 4 X n room with 1x2 Tatami mats. At most 3 Tatami mats may meet at a point.

DATA

1, 4, 4, 2, 3, 3, 3, 5, 5, 6, 8, 8, 11, 13, 14, 19, 21, 25, 32, 35, 44, 53, 60, 76, 88, 104, 129, 148, 180, 217, 252, 309, 365, 432, 526, 617, 741, 891, 1049, 1267, 1508, 1790, 2158, 2557, 3057, 3666, 4347, 5215, 6223, 7404, 8881, 10570, 12619, 15104, 17974

OFFSET

1,2

FORMULA

For n >= 9, a(n) = a(n-3) + a(n-5).

CROSSREFS

Cf. A068929 for incongruent tilings, A068920 for more info.

KEYWORD

easy,nonn

AUTHOR

Dean Hickerson (dean(AT)math.ucdavis.edu), Mar 11 2002

STATUS

approved