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Search: id:A112838
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| A112838 |
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Small-number statistic from the enumeration of domino tilings of a 5-pillow of order n. |
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+0
11
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| 1, 2, 5, 13, 13, 29, 34, 100, 130, 305, 361, 881, 1145, 2906, 3557, 8669, 10693, 26893, 33680, 83360, 102800, 254565, 317165, 790037, 980237, 2428298, 3011265, 7483801, 9301217, 23092857, 28646722, 71093860
(list; graph; listen)
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OFFSET
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0,2
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COMMENT
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A 5-pillow is a generalized Aztec pillow. The 5-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 5 horizontal squares to every 1 vertical square, and steps down with steps of 1 horizontal square to every 1 vertical square.
Plotting A112838(n+2)/A112838(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 5-pillow of order 6 is 1666=7^2*34. A112838(n)=34.
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CROSSREFS
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A112833 breaks down as A112834^2 times A112835, where A112835 is not necessarily square-free.
3-pillows: A112833-A112835; 7-pillows: A112839-A112841; 9-pillows: A112842-A112844.
Sequence in context: A114508 A139023 A067365 this_sequence A111296 A089728 A127987
Adjacent sequences: A112835 A112836 A112837 this_sequence A112839 A112840 A112841
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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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