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A112841 Small-number statistic from the enumeration of domino tilings of a 7-pillow of order n. 12


%S 1,2,5,13,34,34,74,73,193,256,793,1049,2465,2857,6577,8226,21348,

%T 28872,74740,91970,222217,268769,669265,852305,2201945,2805760,

%U 7000777,8636081,21311098,26588770,67091170,85150213

%N Small-number statistic from the enumeration of domino tilings of a 7-pillow of order n.

%C 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.

%C Plotting A112841(n+2)/A112841(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 7-pillow of order 8 is 23353=11^2*193. A112841(n)=193.

%Y A112839 breaks down as A112840^2 times A112841, where A112841 is not necessarily squarefree.

%Y 3-pillows: A112833-A112835; 5-pillows: A112836-A112838; 9-pillows: A112842-A112844.

%K easy,nonn

%O 0,2

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

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Last modified July 25 20:59 EDT 2021. Contains 346294 sequences. (Running on oeis4.)