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Search: id:A112842
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| A112842 |
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Number of domino tilings of a 9-pillow of order n. |
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13
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| 1, 2, 5, 13, 34, 89, 356, 1737, 9065, 49610, 325832, 2795584, 28098632, 310726442, 3877921669, 58896208285, 1083370353616, 22901813128125, 548749450880000, 15471093192996501, 522297110942557556, 20691062026775504896
(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.
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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.
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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: A048575 A099496 A114299 this_sequence A097417 A006801 A114173
Adjacent sequences: A112839 A112840 A112841 this_sequence A112843 A112844 A112845
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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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