0,2

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.

Plotting A112844(n+2)/A112844(n) gives an intriguing damped sine curve.

C. Hanusa (2005). A Gessel-Viennot-Type Method for Cycle Systems with Applications to Aztec Pillows. PhD Thesis. University of Washington, Seattle, USA.

The number of domino tilings of the 9-pillow of order 8 is 9065=7^2*185. A112844(n)=185.

A112842 breaks down as A112843^2 times A112844, where A112844 is not necessarily squarefree.

3-pillows: A112833-A112835; 5-pillows: A112836-A112838; 7-pillows: A112839-A112841.

Sequence in context: A267905 A209230 A103142 * A027933 A141448 A011783

Adjacent sequences: A112841 A112842 A112843 * A112845 A112846 A112847

easy,nonn

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

approved