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Number of ways to tile a 6 X n room with 1x2 Tatami mats. At most 3 Tatami mats may meet at a point.

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`%I #8 Oct 17 2019 11:47:20
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`%S 1,9,6,3,2,2,2,1,1,2,3,4,3,3,3,4,6,6,7,6,7,9,10,13,12,14,15,17,22,22,
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`%T 27,27,31,37,39,49,49,58,64,70,86,88,107,113,128,150,158,193,201,235,
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`%U 263,286,343,359,428,464,521,606,645,771,823,949,1070,1166,1377,1468
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`%N Number of ways to tile a 6 X n room with 1x2 Tatami mats. At most 3 Tatami mats may meet at a point.
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`%C For n >= 12, a(n) = a(n-5) + a(n-7).
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`%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 5.
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`%H <a href="/index/Rec#order_07">Index entries for linear recurrences with constant coefficients</a>, signature (0,0,0,0,1,0,1).
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`%F G.f.: x*(1-2*x^10-6*x^9-11*x^8-6*x^7-7*x^6+x^5+2*x^4+3*x^3+6*x^2+9*x)/(1-x^7-x^5) [From Maksym Voznyy (voznyy(AT)mail.ru), Aug 11 2009]
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`%Y Cf. A068931 for incongruent tilings, A068920 for more info.
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`%K easy,nonn
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`%O 1,2
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`%A _Dean Hickerson_, Mar 11 2002
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`%E G.f. proposed by Maksym Voznyy checked and corrected by R. J. Mathar, Sep 16 2009.
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