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Search: id:A112843
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| A112843 |
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Large-number statistic from the enumeration of domino tilings of a 9-pillow of order n. |
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3
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| 1, 1, 1, 1, 1, 1, 2, 3, 7, 11, 26, 44, 118, 221, 677, 1721, 6884, 21165, 95800, 324693, 1633462, 6253408, 35917622, 161554715, 1151376732, 6387653627, 54325024024, 348582834189, 3376194023305, 24664208882500, 273518249356480
(list; graph; listen)
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OFFSET
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0,7
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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.
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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. A112843(n)=7.
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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: A101173 A005246 A116406 this_sequence A036651 A049454 A095055
Adjacent sequences: A112840 A112841 A112842 this_sequence A112844 A112845 A112846
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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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