

A112843


Largenumber statistic from the enumeration of domino tilings of a 9pillow of order n.


3



1, 1, 1, 1, 1, 1, 2, 3, 7, 11, 26, 44, 118, 221, 677, 1721, 6884, 21165, 95800, 324693, 1633462, 6253408, 35917622, 161554715, 1151376732, 6387653627, 54325024024, 348582834189, 3376194023305, 24664208882500, 273518249356480
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OFFSET

0,7


COMMENTS

A 9pillow is a generalized Aztec pillow. The 9pillow of order n is a rotationallysymmetric 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.


REFERENCES

C. Hanusa (2005). A GesselViennotType Method for Cycle Systems with Applications to Aztec Pillows. PhD Thesis. University of Washington, Seattle, USA.


LINKS

Table of n, a(n) for n=0..30.


EXAMPLE

The number of domino tilings of the 9pillow of order 8 is 9065=7^2*185. A112843(n)=7.


CROSSREFS

A112842 breaks down as A112843^2 times A112844, where A112844 is not necessarily squarefree.
3pillows: A112833A112835; 5pillows: A112836A112838; 7pillows: A112839A112841.
Sequence in context: A294451 A005246 A116406 * A036651 A049454 A095055
Adjacent sequences: A112840 A112841 A112842 * A112844 A112845 A112846


KEYWORD

nonn


AUTHOR

Christopher Hanusa (chanusa(AT)math.binghamton.edu), Sep 21 2005


STATUS

approved



