A112843 Large-number statistic from the enumeration of domino tilings of a 9-pillow of order n.

1, 1, 1, 1, 1, 1, 2, 3, 7, 11, 26, 44, 118, 221, 677, 1721, 6884, 21165, 95800, 324693, 1633462, 6253408, 35917622, 161554715, 1151376732, 6387653627, 54325024024, 348582834189, 3376194023305, 24664208882500, 273518249356480

Offset

0,7

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.

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..30.

Example

The number of domino tilings of the 9-pillow of order 8 is 9065=7^2*185. A112843(n)=7.

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: A005246 A116406 A354540 * A036651 A049454 A095055

Adjacent sequences: A112840 A112841 A112842 * A112844 A112845 A112846

Keyword

nonn

Author

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

Status

approved