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Number of incongruent ways to tile a 5 X 2n room with 1x2 Tatami mats. At most 3 Tatami mats may meet at a point.
4

%I #16 Jun 13 2015 00:50:31

%S 4,2,1,1,1,2,2,3,3,5,5,8,9,13,15,22,26,37,45,63,78,108,136,186,237,

%T 322,414,559,724,973,1267,1697,2219,2964,3888,5183,6815,9071,11949,

%U 15886,20955,27835,36755,48790,64476,85545,113115,150021,198460,263136

%N Number of incongruent ways to tile a 5 X 2n room with 1x2 Tatami mats. At most 3 Tatami mats may meet at a point.

%H R. J. Mathar, <a href="http://arxiv.org/abs/1311.6135">Paving rectangular regions with rectangular tiles,....</a>, arXiv:1311.6135 [math.CO], Table 12.

%H <a href="/index/Rec#order_09">Index entries for linear recurrences with constant coefficients</a>, signature (0, 1, 1, 1, 0, 0, -1, -1, -1).

%F For n >= 12, a(n) = a(n-2) + a(n-3) + a(n-4) - a(n-7) - a(n-8) - a(n-9).

%F G.f.: x*(4+x^10+5*x^9+4*x^8+3*x^7-x^6-2*x^5-6*x^4-5*x^3 -3*x^2+2*x) / ((x^3+x^2-1)*(x^6+x^4-1)). - Maksym Voznyy (voznyy(AT)mail.ru), Aug 11 2009

%F a(n) = sum(A102541(n-k-2, n-2*k-4), k=0..floor((n-4)/2)), n >= 4. - _Johannes W. Meijer_, Aug 24 2013

%t Join[{4,2},LinearRecurrence[{0,1,1,1,0,0,-1,-1,-1},{1,1,1,2,2,3,3,5,5},50]] (* _Harvey P. Dale_, Nov 21 2014 *)

%Y Cf. A068924 for total number of tilings, A068926 for more info.

%Y Cf. A005683.

%K easy,nonn

%O 1,1

%A _Dean Hickerson_, Mar 11 2002

%E G.f. proposed by Maksym Voznyy checked and corrected by _R. J. Mathar_, Sep 16 2009.