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Search: id:A112841
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| A112841 |
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Small-number statistic from the enumeration of domino tilings of a 7-pillow of order n. |
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+0
12
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| 1, 2, 5, 13, 34, 34, 74, 73, 193, 256, 793, 1049, 2465, 2857, 6577, 8226, 21348, 28872, 74740, 91970, 222217, 268769, 669265, 852305, 2201945, 2805760, 7000777, 8636081, 21311098, 26588770, 67091170, 85150213
(list; graph; listen)
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OFFSET
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0,2
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COMMENT
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A 7-pillow is a generalized Aztec pillow. The 7-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 7 horizontal squares to every 1 vertical square, and steps down with steps of 1 horizontal square to every 1 vertical square.
Plotting A112841(n+2)/A112841(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 7-pillow of order 8 is 23353=11^2*193. A112841(n)=193.
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CROSSREFS
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A112839 breaks down as A112840^2 times A112841, where A112841 is not necessarily square-free.
3-pillows: A112833-A112835; 5-pillows: A112836-A112838; 9-pillows: A112842-A112844.
Adjacent sequences: A112838 A112839 A112840 this_sequence A112842 A112843 A112844
Sequence in context: A080888 A052988 A001429 this_sequence A104589 A122024 A027931
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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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