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Search: id:A112835
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| A112835 |
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Small-number statistic from the enumeration of domino tilings of a 3-pillow of order n. |
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+0
12
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| 1, 2, 5, 5, 13, 16, 37, 45, 109, 130, 313, 377, 905, 1088, 2617, 3145, 7561, 9090, 21853, 26269, 63157, 75920, 182525, 219413, 527509, 634114, 1524529, 1832625, 4405969, 5296384, 12733489, 15306833, 36800465, 44237570, 106355317
(list; graph; listen)
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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.
Breaking this sequence into two sequences yields A071101 and A071100, both of which have nice generating functions.
Plotting A112835(n+2)/A112835(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 3-pillow of order 4 is 117=3^2*13. A112835(4)=13.
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CROSSREFS
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A112833 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.
This sequence interleaves A071101 and A071100.
Sequence in context: A138316 A124201 A100953 this_sequence A063786 A121304 A002106
Adjacent sequences: A112832 A112833 A112834 this_sequence A112836 A112837 A112838
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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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