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A248880
Number of tilings of an n X 1 rectangle by tiles of dimension 1 X 1 and 2 X 1 such that every tile shares an equal-length edge with a tile of the same size.
1
1, 0, 1, 1, 2, 1, 4, 3, 7, 7, 13, 14, 24, 28, 45, 56, 86, 111, 165, 218, 317, 426, 611, 831, 1181, 1619, 2286, 3150, 4428, 6123, 8582, 11896, 16641, 23105, 32278, 44865, 62620, 87103, 121499, 169087, 235761, 328214, 457508, 637064, 887857, 1236500, 1723054
OFFSET
0,5
FORMULA
[ 0 1 0 1 0 0 0 ] [1]
[ 0 0 1 0 0 0 0 ] [0]
[ 0 0 1 1 0 0 0 ] [1]
a(n) = [1 0 0 0 0 0 0] * [ 0 0 0 0 1 0 0 ] ^ n * [0], for any n>=0.
[ 0 0 0 0 0 1 0 ] [0]
[ 0 0 0 0 0 0 1 ] [0]
[ 0 1 0 0 0 1 0 ] [1]
G.f.: -(x^2-x+1)*(x^4-x^2+1) / (x^6-x^3+x^2+x-1). - Colin Barker, Mar 05 2015
EXAMPLE
A 3 X 1 rectangle can be tiled in three ways:
+-+-+-+ +-+---+ +---+-+
| | | |, | | | and | | |.
+-+-+-+ +-+---+ +---+-+
The first tiling is acceptable, as every 1 X 1 tile is next to another 1 X 1 tile (and there are no 2 X 1 tiles).
The second and third tilings are not acceptable, as the 1 X 1 tiles are not next to other 1 X 1 tiles.
Hence, a(3)=1.
PROG
(PARI) Vec(-(x^2-x+1)*(x^4-x^2+1)/(x^6-x^3+x^2+x-1) + O(x^100)) \\ Colin Barker, Mar 05 2015
CROSSREFS
Cf. A245596.
Sequence in context: A238544 A101708 A339559 * A026255 A109250 A138236
KEYWORD
nonn,easy
AUTHOR
Paul Tek, Mar 05 2015
STATUS
approved