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Search: id:A112844
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| A112844 |
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Small-number statistic from the enumeration of domino tilings of a 9-pillow of order n. |
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+0
20
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| 1, 2, 5, 13, 34, 89, 89, 193, 185, 410, 482, 1444, 2018, 6362, 8461, 19885, 22861, 51125, 59792, 146749, 195749, 529114, 730465, 1907545, 2350177, 5638489, 6692337, 16167545, 20091490, 51762100, 67753160, 178151440, 229118152
(list; graph; listen)
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OFFSET
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0,2
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COMMENT
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A 9-pillow is a generalized Aztec pillow. The 9-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 9 horizontal squares to every 1 vertical square and steps down with steps of 1 horizontal square to every 1 vertical square.
Plotting A112844(n+2)/A112844(n) gives an intriguing damped sine curve.
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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 9-pillow of order 8 is 9065=7^2*185. A112844(n)=185.
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CROSSREFS
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A112842 breaks down as A112843^2 times A112844, where A112844 is not necessarily square-free.
3-pillows: A112833-A112835; 5-pillows: A112836-A112838; 7-pillows: A112839-A112841.
Sequence in context: A122024 A027931 A103142 this_sequence A027933 A141448 A011783
Adjacent sequences: A112841 A112842 A112843 this_sequence A112845 A112846 A112847
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KEYWORD
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easy,nonn
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AUTHOR
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Christopher Hanusa (chanusa(AT)math.binghamton.edu), Sep 21 2005
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