

A112834


Largenumber statistic from the enumeration of domino tilings of a 3pillow of order n.


5



1, 1, 1, 2, 3, 8, 19, 76, 263, 1584, 8199, 73272, 566401, 7555072, 87000289, 1730799376, 29728075177, 881736342784, 22583659690665, 998900331837728, 38149790451459859, 2516220411436892160, 143302702816187031875
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OFFSET

0,4


COMMENTS

A 3pillow is also called an Aztec pillow. The 3pillow 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 3 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..22.


EXAMPLE

The number of domino tilings of the 3pillow of order 4 is 117=3^2*13. A112834(4)=3.


CROSSREFS

A112833 breaks down as a(n)^2 times A112835, where A112835 is not necessarily squarefree.
5pillows: A112836A112838; 7pillows: A112839A112841; 9pillows: A112842A112844.
Sequence in context: A007999 A006609 A005663 * A042697 A042905 A247568
Adjacent sequences: A112831 A112832 A112833 * A112835 A112836 A112837


KEYWORD

nonn


AUTHOR

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


STATUS

approved



