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Small-number statistic from the enumeration of domino tilings of a 9-pillow of order n.
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%I #4 Jun 01 2010 03:00:00

%S 1,2,5,13,34,89,89,193,185,410,482,1444,2018,6362,8461,19885,22861,

%T 51125,59792,146749,195749,529114,730465,1907545,2350177,5638489,

%U 6692337,16167545,20091490,51762100,67753160,178151440,229118152

%N Small-number statistic from the enumeration of domino tilings of a 9-pillow of order n.

%C A 9-pillow is a generalized Aztec pillow. The 9-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 9 horizontal squares to every 1 vertical square and steps down with steps of 1 horizontal square to every 1 vertical square.

%C Plotting A112844(n+2)/A112844(n) gives an intriguing damped sine curve.

%D C. Hanusa (2005). A Gessel-Viennot-Type Method for Cycle Systems with Applications to Aztec Pillows. PhD Thesis. University of Washington, Seattle, USA.

%e The number of domino tilings of the 9-pillow of order 8 is 9065=7^2*185. A112844(n)=185.

%Y A112842 breaks down as A112843^2 times A112844, where A112844 is not necessarily squarefree.

%Y 3-pillows: A112833-A112835; 5-pillows: A112836-A112838; 7-pillows: A112839-A112841.

%K easy,nonn

%O 0,2

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