A068928 Number of incongruent ways to tile a 3 X 2n room with 1x2 Tatami mats. At most 3 Tatami mats may meet at a point.

2, 2, 2, 4, 5, 9, 12, 21, 30, 51, 76, 127, 195, 322, 504, 826, 1309, 2135, 3410, 5545, 8900, 14445, 23256, 37701, 60813, 98514, 159094, 257608, 416325, 673933, 1089648, 1763581, 2852242, 4615823, 7466468, 12082291, 19546175, 31628466, 51170460, 82798926, 133962621

Offset

1,1

Links

Paolo Xausa, Table of n, a(n) for n = 1..1000

R. J. Mathar, Paving rectangular regions with rectangular tiles,...., arXiv:1311.6135 [math.CO], Table 10.

Index entries for linear recurrences with constant coefficients, signature (1,2,-1,0,-1,-1).

Formula

For n >= 8, a(n) = a(n-1) + 2*a(n-2) - a(n-3) - a(n-5) - a(n-6).

From R. J. Mathar, Aug 30 2008: (Start)

O.g.f.: x*(2-4*x^2-x^4+x^6)/((1-x-x^2)*(1-x^2-x^4)).

a(n) = (A000045(n+1)+A053602(n+1))/2, n>1. (End)

Mathematica

LinearRecurrence[{1, 2, -1, 0, -1, -1}, {2, 2, 2, 4, 5, 9, 12}, 50] (* Paolo Xausa, May 25 2026 *)

Crossrefs

Cf. A068922 for total number of tilings, A068926 for more info.

Essentially the same as A001224.

Cf. A000045, A053602.

Sequence in context: A024405 A230381 A082547 * A326025 A278502 A278501

Adjacent sequences: A068925 A068926 A068927 * A068929 A068930 A068931

Keyword

easy,nonn

Author

Dean Hickerson, Mar 11 2002

Extensions

More terms from Paolo Xausa, May 25 2026

Status

approved