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 A360725 Number of ways to tile an n X n square using oblongs with distinct height x width dimensions. 3
 0, 0, 4, 36, 1056, 31052, 1473944, 87469884 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,3 COMMENTS All possible tilings are counted, including those identical by symmetry. Note that distinct height x width dimensions means that, for example, a 1 x 3 oblong can be used twice, once in a horizonal (1 x 3) and once in a vertical (3 x 1) direction. LINKS Table of n, a(n) for n=1..8. EXAMPLE a(1) = 0 as no distinct oblongs can tile a square with dimensions 1 x 1. a(2) = 0 as no distinct oblongs can tile a square with dimensions 2 x 2. a(3) = 4. There is one tiling, excluding those equivalent by symmetry: . +---+---+---+ | | +---+---+---+ | | + + | | +---+---+---+ . This tiling can occur in 4 different ways, giving 4 ways in total. a(4) = 36. The possible tilings, excluding those equivalent by symmetry, are: . +---+---+---+---+ +---+---+---+---+ +---+---+---+---+ +---+---+---+---+ | | | | | | | | | | | + + + +---+---+---+---+ + +---+---+---+ + +---+---+---+ | | | | | | | | | | | | +---+---+---+---+ + + + + + + + + + | | | | | | | | | | | + + + + +---+---+---+---+ +---+---+ + | | | | | | | | | +---+---+---+---+ +---+---+---+---+ +---+---+---+---+ +---+---+---+---+ . The first tiling can occur in 8 different ways, the second in 4 different ways, the third in 16 different ways and the fourth in 8 different ways. This gives 36 ways in total. CROSSREFS Cf. A360256 (rectangles), A360499, A360498, A182275, A004003, A099390, A065072. Sequence in context: A120605 A337851 A353410 * A173212 A143764 A152287 Adjacent sequences: A360722 A360723 A360724 * A360726 A360727 A360728 KEYWORD nonn,more AUTHOR Scott R. Shannon, Feb 18 2023 STATUS approved

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Last modified September 21 14:54 EDT 2023. Contains 365502 sequences. (Running on oeis4.)