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A245596
Number of tilings of an n X 1 rectangle by tiles of dimension 1 X 1 and 2 X 1 such that every tile is next to a tile of different size.
3
1, 0, 0, 2, 1, 1, 4, 3, 4, 8, 9, 12, 19, 24, 33, 48, 64, 88, 124, 169, 233, 324, 445, 614, 850, 1171, 1616, 2233, 3080, 4251, 5870, 8100, 11180, 15434, 21301, 29401, 40584, 56015, 77316, 106720, 147301, 203316, 280635, 387352, 534653
OFFSET
0,4
FORMULA
[0 1 0 0 1 0 0] [1]
[0 0 1 0 0 0 0] [0]
[0 0 0 1 0 0 0] [0]
a(n) = [1 0 0 0 0 0 0] * [0 0 0 0 1 0 1]^n * [1], for any n>=0.
[0 0 0 0 0 1 0] [0]
[0 0 0 0 0 0 1] [0]
[0 1 1 0 0 0 0] [1]
G.f.: (x^6+x^3+1)/(-x^6-x^5-x^4-x^3+1) = -(x^6+x^3+1)/((x^2+x+1)*(x^4+x-1)). - Colin Barker, Jul 27 2014
a(n) = a(n-3)+a(n-4)+a(n-5)+a(n-6) for n>6. - Colin Barker, Jul 28 2014
EXAMPLE
A 3 X 1 rectangle can be tiled in three ways:
+-+-+-+ +-+---+ +---+-+
| | | |, | | | and | | |.
+-+-+-+ +-+---+ +---+-+
The first tiling is not acceptable, as none of the 1 X 1 tiles is next to a 2 X 1 tile.
The second and third tilings are acceptable, as every 1 X 1 tile is next to a 2 X 1 tile and vice versa.
Hence, a(3)=2.
PROG
(PARI) Vec(-(x^6+x^3+1)/((x^2+x+1)*(x^4+x-1)) + O(x^100)) \\ Colin Barker, Jul 28 2014
CROSSREFS
Cf. A230096.
Sequence in context: A240769 A357320 A174455 * A326611 A083293 A350912
KEYWORD
nonn,easy
AUTHOR
Paul Tek, Jul 27 2014
STATUS
approved