%I A112833
%S A112833 1,2,5,20,117,1024,13357,259920,7539421,326177280,21040987113,
%T A112833 2024032315968,290333133984905,62102074862600192,19808204598680574457,
%U A112833 9421371079480456587520,6682097668647718038428569
%N A112833 Number of domino tilings of a 3-pillow of order n.
%C A112833 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 A112833 C. Hanusa (2005). A Gessel-Viennot-Type Method for Cycle Systems with 
               Applications to Aztec Pillows. PhD Thesis. University of Washington, 
               Seattle, USA.
%e A112833 The number of domino tilings of the 3-pillow of order 4 is 117=3^2*13.
%Y A112833 This sequence breaks down as A112834^2 times A112835, where A112835 is 
               not necessarily square-free.
%Y A112833 5-pillows: A112836-A112838; 7-pillows: A112839-A112841; 9-pillows: A112842-A112844.
%Y A112833 Related to A071101 and A071100.
%Y A112833 Sequence in context: A052850 A000130 A009599 this_sequence A144503 A012321 
               A012519
%Y A112833 Adjacent sequences: A112830 A112831 A112832 this_sequence A112834 A112835 
               A112836
%K A112833 nonn
%O A112833 0,2
%A A112833 Christopher Hanusa (chanusa(AT)math.binghamton.edu), Sep 21 2005