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%I #6 Sep 17 2023 00:26:11
%S 1,2,5,13,52,261,1666,14400,159250,2308545,43718544,1079620569,
%T 34863330980,1466458546176,80646187346132,5787269582487581,
%U 541901038236234048,66279540183479379277,10578427028263503488000
%N Number of domino tilings of a 5-pillow of order n.
%C A 5-pillow is a generalized Aztec pillow. The 5-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 5 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 5-pillow of order 6 is 1666=7^2*34.
%Y A112836 can be decomposed as A112837^2 times A112838, where A112838 is not necessarily squarefree.
%Y 3-pillows: A112833-A112835; 7-pillows: A112839-A112841; 9-pillows: A112842-A112844.
%K nonn
%O 0,2
%A Christopher Hanusa (chanusa(AT)math.binghamton.edu), Sep 21 2005