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A112841
Small-number statistic from the enumeration of domino tilings of a 7-pillow of order n.
12
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
OFFSET
0,2
COMMENTS
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.
REFERENCES
C. Hanusa (2005). A Gessel-Viennot-Type Method for Cycle Systems with Applications to Aztec Pillows. PhD Thesis. University of Washington, Seattle, USA.
EXAMPLE
The number of domino tilings of the 7-pillow of order 8 is 23353=11^2*193. A112841(n)=193.
CROSSREFS
A112839 breaks down as A112840^2 times A112841, where A112841 is not necessarily squarefree.
3-pillows: A112833-A112835; 5-pillows: A112836-A112838; 9-pillows: A112842-A112844.
Sequence in context: A278134 A271940 A273721 * A104589 A154101 A122024
KEYWORD
easy,nonn
AUTHOR
Christopher Hanusa (chanusa(AT)math.binghamton.edu), Sep 21 2005
STATUS
approved