A112837 Large-number statistic from the enumeration of domino tilings of a 5-pillow of order n.

1, 1, 1, 1, 2, 3, 7, 12, 35, 87, 348, 1107, 5518, 22464, 150574, 817057, 7118856, 49644383, 560434040, 5142118400, 76370120248, 914476059335, 17638655014128, 274908897964359, 6936239946318204, 141510942505315328

Offset

0,5

Comments

A 5-pillow is a generalized Aztec pillow. The 5-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 5 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..25.

Example

The number of domino tilings of the 5-pillow of order 6 is 1666=7^2*34. A112837(n)=7.

Crossrefs

A112833 breaks down as A112834^2 times A112835, where A112835 is not necessarily squarefree.

3-pillows: A112833-A112835; 7-pillows: A112839-A112841; 9-pillows: A112842-A112844.

Sequence in context: A034786 A080107 A056156 * A056355 A056356 A084708

Adjacent sequences: A112834 A112835 A112836 * A112838 A112839 A112840

Keyword

nonn

Author

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

Status

approved