A112834 Large-number statistic from the enumeration of domino tilings of a 3-pillow of order n.

1, 1, 1, 2, 3, 8, 19, 76, 263, 1584, 8199, 73272, 566401, 7555072, 87000289, 1730799376, 29728075177, 881736342784, 22583659690665, 998900331837728, 38149790451459859, 2516220411436892160, 143302702816187031875

Offset

0,4

Comments

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.

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..22.

Example

The number of domino tilings of the 3-pillow of order 4 is 117=3^2*13. A112834(4)=3.

Crossrefs

A112833 breaks down as a(n)^2 times A112835, where A112835 is not necessarily squarefree.

5-pillows: A112836-A112838; 7-pillows: A112839-A112841; 9-pillows: A112842-A112844.

Sequence in context: A007999 A006609 A005663 * A042697 A042905 A247568

Adjacent sequences: A112831 A112832 A112833 * A112835 A112836 A112837

Keyword

nonn

Author

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

Status

approved