A112840 Large-number statistic from the enumeration of domino tilings of a 7-pillow of order n.

1, 1, 1, 1, 1, 2, 3, 7, 11, 28, 51, 154, 389, 1556, 4833, 22477, 80532, 440512, 1916580, 13388593, 73763989, 632754664, 4175659899, 42606281476, 336819337955, 4181786155008, 40981322633555, 630857431556758, 7576627032674784

Offset

0,6

Comments

A 7-pillow is a generalized Aztec pillow. The 7-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 7 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..28.

Example

The number of domino tilings of the 7-pillow of order 8 is 23353=11^2*193. A112840(n)=11.

Crossrefs

A112839 breaks down as A112840^2 times A112841, where A112841 is not necessarily squarefree.

3-pillows: A112833-A112835; 5-pillows: A112836-A112838; 9-pillows: A112842-A112844.

Sequence in context: A107858 A214938 A143926 * A014981 A227885 A096362

Adjacent sequences: A112837 A112838 A112839 * A112841 A112842 A112843

Keyword

nonn

Author

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

Status

approved