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A359703 Number of fillomino dissections of a 2 X n rectangle. 1
1, 1, 5, 33, 138, 715, 3524, 17119, 84655, 416723, 2047650, 10072806, 49542408, 243701785, 1198732022, 5895900754, 28999718642, 142641530115, 701610208573, 3450988507136, 16974245195432, 83490673950264, 410663317558386, 2019918477187441, 9935315439670326 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,3
COMMENTS
A fillomino dissection of a rectangle is a tiling by polyominoes in which no two polyominoes of the same size are adjacent.
The sequence a(n+1)/a(n) appears to converge rapidly to 4.91867 12250 37424 13083 06703 91572 28440 1... (with a baffling sequence of sign changes in a(n+2)a(n)-a(n+1)^2). - Don Knuth, Jan 15 2023
REFERENCES
Donald E. Knuth, The Art of Computer Programming, exercise in Section 7.2.2.3 (in preparation).
LINKS
Don Knuth, fillomino2xn.m
Wikipedia, Fillomino
EXAMPLE
For n=2 the a(2)=5 dissections are
13 31 33 33 44
33 33 13 31 44
CROSSREFS
The fillomino dissections of a 1 X n rectangle are Carlitz compositions (sequence A003242).
Sequence in context: A211059 A292000 A146263 * A255943 A270222 A270279
KEYWORD
nonn
AUTHOR
Don Knuth, Jan 11 2023
EXTENSIONS
a(20)-a(24) from Alois P. Heinz, Jan 12 2023
STATUS
approved

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Last modified June 5 12:45 EDT 2023. Contains 363136 sequences. (Running on oeis4.)