A068930 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, 2, 1, 1, 1, 2, 2, 3, 3, 5, 5, 8, 9, 13, 15, 22, 26, 37, 45, 63, 78, 108, 136, 186, 237, 322, 414, 559, 724, 973, 1267, 1697, 2219, 2964, 3888, 5183, 6815, 9071, 11949, 15886, 20955, 27835, 36755, 48790, 64476, 85545, 113115, 150021, 198460, 263136

Offset: 1

Author

Dean Hickerson, Mar 11 2002

Keywords

• easy
• nonn

Links

• R. J. Mathar, Paving rectangular regions with rectangular tiles,...., arXiv:1311.6135 [math.CO], Table 12.
• Index entries for linear recurrences with constant coefficients, signature (0, 1, 1, 1, 0, 0, -1, -1, -1).

Crossrefs

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

Cf. A005683.

Programs

Mathematica

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 *)

Formula

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

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

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

Extensions

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