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%I #4 Jun 01 2010 03:00:00
%S 1,1,1,2,3,8,19,76,263,1584,8199,73272,566401,7555072,87000289,
%T 1730799376,29728075177,881736342784,22583659690665,998900331837728,
%U 38149790451459859,2516220411436892160,143302702816187031875
%N Large-number statistic from the enumeration of domino tilings of a 3-pillow of order n.
%C A 3-pillow is also called an Aztec pillow. The 3-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 3 horizontal squares to every 1 vertical square and steps down with steps of 1 horizontal square to every 1 vertical square.
%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 3-pillow of order 4 is 117=3^2*13. A112834(4)=3.
%Y A112833 breaks down as a(n)^2 times A112835, where A112835 is not necessarily squarefree.
%Y 5-pillows: A112836-A112838; 7-pillows: A112839-A112841; 9-pillows: A112842-A112844.
%K nonn
%O 0,4
%A Christopher Hanusa (chanusa(AT)math.binghamton.edu), Sep 21 2005
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