%I A112842
%S A112842 1,2,5,13,34,89,356,1737,9065,49610,325832,2795584,28098632,310726442,
%T A112842 3877921669,58896208285,1083370353616,22901813128125,548749450880000,
%U A112842 15471093192996501,522297110942557556,20691062026775504896
%N A112842 Number of domino tilings of a 9-pillow of order n.
%C A112842 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.
%D A112842 C. Hanusa (2005). A Gessel-Viennot-Type Method for Cycle Systems with 
               Applications to Aztec Pillows. PhD Thesis. University of Washington, 
               Seattle, USA.
%e A112842 The number of domino tilings of the 9-pillow of order 8 is 9065=7^2*185.
%Y A112842 A112842 breaks down as A112843^2 times A112844, where A112844 is not 
               necessarily square-free.
%Y A112842 3-pillows: A112833-A112835; 5-pillows: A112836-A112838; 7-pillows: A112839-A112841.
%Y A112842 Sequence in context: A048575 A099496 A114299 this_sequence A097417 A006801 
               A114173
%Y A112842 Adjacent sequences: A112839 A112840 A112841 this_sequence A112843 A112844 
               A112845
%K A112842 nonn
%O A112842 0,2
%A A112842 Christopher Hanusa (chanusa(AT)math.binghamton.edu), Sep 21 2005