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Search: id:A112833
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| A112833 |
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Number of domino tilings of a 3-pillow of order n. |
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20
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| 1, 2, 5, 20, 117, 1024, 13357, 259920, 7539421, 326177280, 21040987113, 2024032315968, 290333133984905, 62102074862600192, 19808204598680574457, 9421371079480456587520, 6682097668647718038428569
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OFFSET
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0,2
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COMMENT
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A 3-pillow is also called an Aztec pillow. The 3-pillow of order n is a rotationally-symmetric region. It has a 2 X 2n central band of squares, and then steps up from this band with steps of 3 horizontal squares to every 1 vertical square, and steps down with steps of 1 horizontal square to every 1 vertical square.
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REFERENCES
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C. Hanusa (2005). A Gessel-Viennot-Type Method for Cycle Systems with Applications to Aztec Pillows. PhD Thesis. University of Washington, Seattle, USA.
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EXAMPLE
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The number of domino tilings of the 3-pillow of order 4 is 117=3^2*13.
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CROSSREFS
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This sequence breaks down as A112834^2 times A112835, where A112835 is not necessarily square-free.
5-pillows: A112836-A112838; 7-pillows: A112839-A112841; 9-pillows: A112842-A112844.
Related to A071101 and A071100.
Adjacent sequences: A112830 A112831 A112832 this_sequence A112834 A112835 A112836
Sequence in context: A052850 A000130 A009599 this_sequence A012321 A012519 A076795
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KEYWORD
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nonn
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AUTHOR
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Christopher Hanusa (chanusa(AT)math.binghamton.edu), Sep 21 2005
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