A112844 Small-number statistic from the enumeration of domino tilings of a 9-pillow of order n.

1, 2, 5, 13, 34, 89, 89, 193, 185, 410, 482, 1444, 2018, 6362, 8461, 19885, 22861, 51125, 59792, 146749, 195749, 529114, 730465, 1907545, 2350177, 5638489, 6692337, 16167545, 20091490, 51762100, 67753160, 178151440, 229118152

Offset

0,2

Comments

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.

References

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

Links

Table of n, a(n) for n=0..32.

Example

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

Crossrefs

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

Keyword

easy,nonn

Author

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

Status

approved